A096034 Triangle read by rows: T(n,k) = (n+1,k)-th element of (M^3-M)/2, where M is the infinite lower Pascal's triangle matrix, 1<=k<=n.

1, 4, 2, 13, 12, 3, 40, 52, 24, 4, 121, 200, 130, 40, 5, 364, 726, 600, 260, 60, 6, 1093, 2548, 2541, 1400, 455, 84, 7, 3280, 8744, 10192, 6776, 2800, 728, 112, 8, 9841, 29520, 39348, 30576, 15246, 5040, 1092, 144, 9, 29524, 98410, 147600, 131160, 76440

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

Triangle begins:
1
4 2
13 12 3
40 52 24 4
121 200 130 40 5
364 726 600 260 60 6

Maple

P:= proc(n) option remember; local M; M:= Matrix(n, (i, j)-> binomial(i-1, j-1)); (M^3-M)/2 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 = 10; M = Table[If[k > n, 0, Binomial[n, k]], {n, 0, max}, {k, 0, max} ];
T = (M.M.M - M)/2;
Table[T[[n + 1]][[1 ;; n]], {n, 1, max}] // Flatten (* Jean-François Alcover, May 24 2016 *)

Crossrefs

Cf. A007318. First column gives A003462. Row sums give A006516.

Sequence in context: A180194 A193853 A213853 * A193849 A064308 A330314

Adjacent sequences: A096031 A096032 A096033 * A096035 A096036 A096037

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

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

Status

approved