A080249 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A080249

Stirling-like number triangle defined by the sequence A000292=C(n+3,3).

1, 1, 1, 1, 5, 1, 1, 21, 15, 1, 1, 85, 171, 35, 1, 1, 341, 1795, 871, 70, 1, 1, 1365, 18291, 19215, 3321, 126, 1, 1, 5461, 184275, 402591, 135450, 10377, 210, 1, 1, 21845, 1848211, 8236095, 5143341, 716562, 28017, 330, 1, 1, 87381, 18503955, 166570111, 188253030, 45270813, 3069990, 67617, 495, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

Columns include A002450, A016225. The defining sequence A000292=C(n+3,3) is the sequence of partial sums of the defining sequence for number triangle A080248.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = T(n-1,k-1) + A000292(k)*T(n-1,k). Columns are generated by 1/product{k=0..n, 1-C(k+3,3)*x}.

EXAMPLE

Triangle begins:

1, 1;

1, 5, 1;

1, 21, 15, 1;

1, 85, 171, 35, 1;

1, 341, 1795, 871, 70, 1;

1, 1365, 18291, 19215, 3321, 126, 1;