A096042 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.
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
Offset: 1
Examples
Triangle begins: 1 9 2 73 27 3 585 292 54 4 4681 2925 730 90 5 37449 28086 8775 1460 135 6
Programs
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Maple
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
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 *)
Extensions
Edited with more terms by Alois P. Heinz, Oct 07 2009