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A095799 Bell triangle A011971 squared. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 24 2016 *)

CROSSREFS

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

Sequence in context: A041435 A136210 A041819 * 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

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Last modified June 24 09:12 EDT 2021. Contains 345416 sequences. (Running on oeis4.)