login
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
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
1,2
EXAMPLE
Triangle begins:
1;
7, 2;
43, 21, 3;
259, 172, 42, 4;
1555, 1295, 430, 70, 5;
9331, 9330, 3885, 860, 105, 6;
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 *)
CROSSREFS
Cf. A007318. First column gives A003464. Row sums give A016130.
Sequence in context: A222555 A246799 A248189 * A038268 A100983 A350621
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 17 2004
EXTENSIONS
Edited with more terms by Alois P. Heinz, Oct 07 2009
STATUS
approved