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A154109 Convolution triangle by rows, A004736 * (A154108 * 0^n-k)); 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 (list; table; graph; refs; listen; history; text; internal format)
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 =

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

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Last modified October 21 18:11 EDT 2018. Contains 316427 sequences. (Running on oeis4.)