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A154109 Convolution triangle by rows, A004736 * (A154108 * 0^(n-k)); row sums = Bell numbers.

%I A154109 #5 Dec 26 2023 13:06:35
%S A154109 1,2,0,3,0,2,4,0,4,7,5,0,6,14,27,6,0,8,21,54,114,7,0,10,28,81,228,523,
%T A154109 8,0,12,35,108,342,1046,2589,9,0,14,42,135,456,1569,5178,13744,10,0,
%U A154109 16,49,162,570,2092,7767,27488,77821
%N A154109 Convolution triangle by rows, A004736 * (A154108 * 0^(n-k)); row sums = Bell numbers.
%C A154109 Row sums = Bell numbers, A000110 starting (1, 2, 5, 15, 52, 203, 877,...).
%F A154109 A004736 * (A154108 * 0^(n-k)); where A004736 = an infinite lower triangular
%F A154109 matrix with (1,2,3,...) in every column and (A154108 * 0^(n-k)) = a matrix
%F A154109 with A154108 (1, 0, 2, 7, 27, 114, 523, 2589...) as the main diagonal
%F A154109 and the rest zeros.
%e A154109 First few rows of the triangle =
%e A154109 1;
%e A154109 2, 0;
%e A154109 3, 0, 2;
%e A154109 4, 0, 4, 7;
%e A154109 5, 0, 6, 14, 27;
%e A154109 6, 0, 8, 21, 54, 114;
%e A154109 7, 0, 10, 28, 81, 228, 523;
%e A154109 8, 0, 12, 35, 108, 342, 1046, 2589;
%e A154109 9, 0, 14, 42, 135, 456, 1569, 5178, 13744;
%e A154109 10, 0, 16, 49, 162, 570, 2092, 7767, 27488, 77821;
%e A154109 ...
%e A154109 Row 5 = (5, 0, 6, 14, 27), sum = A000110(5) = 52 = termwise products of
%e A154109 (5, 4, 3, 2, 1) and (1, 0, 2, 7, 27).
%Y A154109 Cf. A154108, A000110.
%K A154109 nonn,tabl
%O A154109 1,2
%A A154109 _Gary W. Adamson_, Jan 04 2009