A154109 - OEIS

A154109

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

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^(n-k)); where A004736 = an infinite lower triangular

matrix with (1,2,3,...) in every column and (A154108 * 0^(n-k)) = 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 =

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