A095799 Bell triangle A011971 squared.

1, 3, 4, 15, 21, 25, 107, 149, 200, 225, 1054, 1420, 1909, 2479, 2704, 13684, 17814, 23313, 30439, 38505, 41209, 224071, 283592, 360853, 461015, 587641, 727920, 769129, 4471699, 5535812, 6881856, 8590990, 10758160, 13443289, 16370471, 17139600

Offset: 1

Author

Gary W. Adamson, Jun 06 2004

Keywords

• nonn
• tabl

Examples

			T(3,2) = 21, because M = [1; 1 2; 2 3 5; ...], M^2 = [1; 3 4; 15 21 25; ...] and M^2[3,2] = 21.
Triangle begins:
:     1;
:     3,     4;
:    15,    21,    25;
:   107,   149,   200,   225;
:  1054,  1420,  1909,  2479,  2704;
: 13684, 17814, 23313, 30439, 38505, 41209;
		

Links

• Alois P. Heinz, Rows n = 1..45, flattened

Crossrefs

Cf. A011971. Diagonal gives A001247 for n>0.

Programs

Maple

with(combinat): A:= proc(n, k) option remember; `if`(k<=n, add(binomial(k, i) *bell(n-k+i), i=0..k), 0) end: M:= proc(n) option remember; Matrix(n, (i, j)-> A(i-1, j-1)) end: T:= (n, k)-> (M(n)^2)[n, k]: seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, Oct 12 2009

Mathematica

max = 10; M = Table[If[k > n, 0, Sum[Binomial[k, i] BellB[n-k+i], {i, 0, k} ]], {n, 0, max-1}, {k, 0, max-1}];
T = M.M;
Table[T[[n]][[1 ;; n]], {n, 1, max}] // Flatten (* Jean-François Alcover, May 24 2016 *)

Formula

Let M = the Bell triangle (A011971) as an infinite lower triangle matrix. Then T(n,k) = M^2[n,k].

Extensions

Edited, corrected and extended by Alois P. Heinz, Oct 12 2009