Revision History for A187783
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#64 by R. J. Mathar at Wed Jun 21 08:43:45 EDT 2023
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#63 by R. J. Mathar at Wed Jun 21 08:30:31 EDT 2023
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#62 by R. J. Mathar at Wed Jun 21 04:49:49 EDT 2023
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#61 by R. J. Mathar at Wed Jun 21 04:39:52 EDT 2023
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| CROSSREFS
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Cf. A089759 (transposed), A141906, (subtriangle), A120666. (subtriangle transposed), A060538 (1st row/colmn removed).
Another version is A089759.
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| STATUS
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approved
editing
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#60 by Michel Marcus at Wed Dec 28 04:08:16 EST 2022
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#59 by Joerg Arndt at Wed Dec 28 02:35:38 EST 2022
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#58 by Michel Marcus at Mon Dec 26 23:59:30 EST 2022
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Discussion
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| Wed Dec 28
| 02:33
| Joerg Arndt: gamma(k*(n-k)+1) wants to be factorial(k*(n-k)) ?
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| 02:35
| Joerg Arndt: OK, now I know
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#57 by Michel Marcus at Mon Dec 26 23:59:26 EST 2022
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| LINKS
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T. Chappell, A. Lascoux, S. Ole Warnaar, and W. Zudilin, <a href="http://arxiv.org/abs/1112.3130">Logarithmic and complex constant term identities</a>, arXiv:1112.3130 [math.CO], 2012.
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| STATUS
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proposed
editing
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#56 by G. C. Greubel at Mon Dec 26 23:46:50 EST 2022
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#55 by G. C. Greubel at Mon Dec 26 23:42:09 EST 2022
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| COMMENTS
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m\n :0 1 2 3 4 5
m
0 : 1 1 1 1 1 1 ... A000012;
1 : 1 1 1 1 1 1 ... A000012;
2 : 1 2 6 20 70 252 ... A000984;
3 : 1 6 90 1680 34650 756756 ... A006480;
4 : 1 24 2520 369600 63063000 11732745024 ... A008977;
5 : 1 120 113400 168168000 305540235000 623360743125120 ... A008978;
6 : 1 720 7484400 137225088000 3246670537110000 88832646059788350720 ... A008979;
with columns: A000142 (n=1), A000680 (n=2), A014606 (n=3), A014608 (n=4), A014609 (n=5).
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| FORMULA
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T(m,n) = (m*n)!/(n!^!)^m)..
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| MATHEMATICA
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T[n_, k_] := (_]:= (k*n)!/(n!)^k; Table[T[n, k - -n], {k, 9}, {n, 0, k - -1}] // }]//Flatten
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| PROG
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(Magma) [Factorial(k*(n-k))/(Factorial(n-k))^k: k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 26 2022
(SageMath)
def A187783(n, k): return gamma(k*(n-k)+1)/(factorial(n-k))^k
flatten([[A187783(n, k) for k in range(n+1)] for n in range(11)]) # G. C. Greubel, Dec 26 2022
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| CROSSREFS
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Rows: A000012, A000984, A006480, A006480, A008978, A008979, A071549, A071550, A071551, A071552.
Columns: A000012, A000142, A000680, A014606, A014608, A014609, A248814, A172603, A172609, A172613.
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| STATUS
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approved
editing
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Discussion
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| Mon Dec 26
| 23:46
| G. C. Greubel: In editing mode the screen is wide and makes the array look like it should. In the published view the array wraps and loses the nice appeal. Removing column 5 could fix this.
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