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

1,2

Links

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

Formula

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

Example

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;

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 *)

Crossrefs

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

Sequence in context: A136210 A041819 A369910 * A109926 A272514 A065942

Adjacent sequences: A095796 A095797 A095798 * A095800 A095801 A095802

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 06 2004

Extensions

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

Status

approved