A096039 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^5-M)/4, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 6, 2, 31, 18, 3, 156, 124, 36, 4, 781, 780, 310, 60, 5, 3906, 4686, 2340, 620, 90, 6, 19531, 27342, 16401, 5460, 1085, 126, 7, 97656, 156248, 109368, 43736, 10920, 1736, 168, 8, 488281, 878904, 703116, 328104, 98406, 19656, 2604, 216, 9, 2441406

Offset: 1

Author

Gary W. Adamson, Jun 17 2004

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
6,       2;
31,     18,    3;
156,   124,   36,   4;
781,   780,  310,  60,  5;
3906, 4686, 2340, 620, 90, 6;
		

Crossrefs

Cf. A007318. First column gives A003463. Row sums give A016129.

Programs

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^5-M)/4 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

Mathematica

max = 11; M = Table[If[k > n, 0, Binomial[n, k]], {n, 0, max}, {k, 0, max} ];
T = (MatrixPower[M, 5] - M)/4;
Table[T[[n + 1]][[1 ;; n]] , {n, 1, max}] // Flatten (* Jean-François Alcover, May 24 2016 *)

Extensions

Edited with more terms by Alois P. Heinz, Oct 07 2009