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A095799 Bell triangle A011971 squared.

%I A095799 #17 May 24 2016 03:05:50
%S A095799 1,3,4,15,21,25,107,149,200,225,1054,1420,1909,2479,2704,13684,17814,
%T A095799 23313,30439,38505,41209,224071,283592,360853,461015,587641,727920,
%U A095799 769129,4471699,5535812,6881856,8590990,10758160,13443289,16370471,17139600
%N A095799 Bell triangle A011971 squared.
%H A095799 Alois P. Heinz, <a href="/A095799/b095799.txt">Rows n = 1..45, flattened</a>
%F A095799 Let M = the Bell triangle (A011971) as an infinite lower triangle matrix. Then T(n,k) = M^2[n,k].
%e A095799 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.
%e A095799 Triangle begins:
%e A095799 :     1;
%e A095799 :     3,     4;
%e A095799 :    15,    21,    25;
%e A095799 :   107,   149,   200,   225;
%e A095799 :  1054,  1420,  1909,  2479,  2704;
%e A095799 : 13684, 17814, 23313, 30439, 38505, 41209;
%p A095799 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
%t A095799 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 A095799 T = M.M;
%t A095799 Table[T[[n]][[1 ;; n]], {n, 1, max}] // Flatten (* _Jean-François Alcover_, May 24 2016 *)
%Y A095799 Cf. A011971. Diagonal gives A001247 for n>0.
%K A095799 nonn,tabl
%O A095799 1,2
%A A095799 _Gary W. Adamson_, Jun 06 2004
%E A095799 Edited, corrected and extended by _Alois P. Heinz_, Oct 12 2009