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A096042
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Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^8-M)/7, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.
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1
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1, 9, 2, 73, 27, 3, 585, 292, 54, 4, 4681, 2925, 730, 90, 5, 37449, 28086, 8775, 1460, 135, 6, 299593, 262143, 98301, 20475, 2555, 189, 7, 2396745, 2396744, 1048572, 262136, 40950, 4088, 252, 8, 19173961, 21570705, 10785348, 3145716, 589806
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Triangle begins:
1
9 2
73 27 3
585 292 54 4
4681 2925 730 90 5
37449 28086 8775 1460 135 6
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MAPLE
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P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^8-M)/7 end: T:= (n, k)-> P(n+1)[n+1, k]: seq(seq(T(n, k), k=1..n), n=1..11); # Alois P. Heinz, Oct 07 2009
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MATHEMATICA
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P[n_] := P[n] = With[{M = Array[Binomial[#1-1, #2-1]&, {n, n}]}, (MatrixPower[M, 8] - M)/7]; T[n_, k_] := P[n+1][[n+1, k]]; Table[ Table[T[n, k], {k, 1, n}], {n, 1, 11}] // Flatten (* Jean-François Alcover, Jan 28 2015, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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