A096040 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^6-M)/5, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 7, 2, 43, 21, 3, 259, 172, 42, 4, 1555, 1295, 430, 70, 5, 9331, 9330, 3885, 860, 105, 6, 55987, 65317, 32655, 9065, 1505, 147, 7, 335923, 447896, 261268, 87080, 18130, 2408, 196, 8, 2015539, 3023307, 2015532, 783804, 195930, 32634, 3612, 252, 9

Offset: 1

Author

Gary W. Adamson, Jun 17 2004

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
7,       2;
43,     21,    3;
259,   172,   42,   4;
1555, 1295,  430,  70,   5;
9331, 9330, 3885, 860, 105, 6;
		

Crossrefs

Cf. A007318. First column gives A003464. Row sums give A016130.

Programs

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^6-M)/5 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, 6] - M)/5;
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