

A154109


Convolution triangle by rows, A004736 * (A154108 * 0^nk)); row sums = Bell numbers.


2



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, 8, 0, 12, 35, 108, 342, 1046, 2589, 9, 0, 14, 42, 135, 456, 1569, 5178, 13744, 10, 0, 16, 49, 162, 570, 2092, 7767, 27488, 77821
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OFFSET

1,2


COMMENTS

Row sums = Bell numbers, A000110 starting (1, 2, 5, 15, 52, 203, 877,...).


LINKS

Table of n, a(n) for n=1..55.


FORMULA

A004736 * (A154108 * 0^(nk)); where A004736 = an infinite lower triangular
matrix with (1,2,3,...) in every column and (A154108 * 0^(nk)) = a matrix
with A154108 (1, 0, 2, 7, 27, 114, 523, 2589...) as the main diagonal
and the rest zeros.


EXAMPLE

First few rows of the triangle =
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;
8, 0, 12, 35, 108, 342, 1046, 2589;
9, 0, 14, 42, 135, 456, 1569, 5178, 13744;
10, 0, 16, 49, 162, 570, 2092, 7767, 27488, 77821;
...
Row 5 = (5, 0, 6, 14, 27), sum = A000110(5) = 52 = termwise products of
(5, 4, 3, 2, 1) and (1, 0, 2, 7, 27).


CROSSREFS

Cf. A154108, A000110
Sequence in context: A127460 A274021 A303711 * A011374 A298645 A243319
Adjacent sequences: A154106 A154107 A154108 * A154110 A154111 A154112


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jan 04 2009


STATUS

approved



