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A257200
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a(n) = n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720.
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6
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1, 6, 22, 63, 154, 336, 672, 1254, 2211, 3718, 6006, 9373, 14196, 20944, 30192, 42636, 59109, 80598, 108262, 143451, 187726, 242880, 310960, 394290, 495495, 617526, 763686, 937657, 1143528, 1385824, 1669536, 2000152, 2383689, 2826726, 3336438, 3920631, 4587778, 5347056, 6208384, 7182462
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OFFSET
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1,2
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COMMENTS
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Antidiagonal sums of the array of 4-dimensional solid numbers shown in Table 3 of Sardelis and Valahas paper (see also Example field).
See A257199 (second comment) for the general formula of this type of numbers: the sequence correspond to the case j = 4.
Binomial transform of (1, 5, 11, 14, 11, 5, 1, 0, 0, 0, ...). - Gary W. Adamson, Aug 26 2015
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LINKS
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FORMULA
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G.f.: x*(-1 + x - x^2)/(-1 + x)^7.
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EXAMPLE
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Array in Comments begins:
1, 5, 15, 35, 70, 126, 210, 330, ...
1, 6, 20, 50, 105, 196, 336, 540, ...
1, 7, 25, 65, 140, 266, 462, 750, ...
1, 8, 30, 80, 175, 336, 588, 960, ...
1, 9, 35, 95, 210, 406, 714, 1170, ...
1, 10, 40, 110, 245, 476, 840, 1380, ...
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MATHEMATICA
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Table[n (n + 1) (n + 2) (n + 3) (n^2 + 3n + 26)/720, {n, 40}]
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PROG
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(Magma) [n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720: n in [1..40]]; // Vincenzo Librandi, Apr 18 2015
(PARI) first(m)=vector(m, i, i*(i+1)*(i+2)*(i+3)*(i^2+3*i+26)/720) \\ Anders Hellström, Aug 26 2015
(PARI) Vec(x*(-1 + x - x^2)/(-1 + x)^7 + O(x^40)) \\ Michel Marcus, Aug 27 2015
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CROSSREFS
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See A080852 for another version of the array.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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