A153199 - OEIS

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A153199

Triangle read by rows, A007318 * A153198.

1, 1, 1, 1, 2, 2, 1, 3, 6, 5, 1, 4, 12, 20, 14, 1, 5, 20, 50, 70, 43, 1, 6, 30, 100, 210, 258, 143, 1, 7, 42, 175, 490, 903, 1001, 509, 1, 8, 56, 280, 980, 2408, 4004, 4072, 1922, 1, 9, 72, 420, 1764, 5418, 12012, 18324, 17298, 7651

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

OFFSET

0,5

COMMENTS

Row sums = A153197 starting (1, 2, 5, 15, 51, 189, 748, 3138,...).

Right border = A006789: (1, 1, 2, 5, 14, 43, 143, 509, 1922,...).

LINKS

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

FORMULA

Binomial transform of triangle A153198, where A153198 = an infinite lower triangular matrix with the Bessel numbers A006789 as the main diagonal and the rest 0's.

EXAMPLE

First few rows of the triangle =

1, 1;

1, 2, 2;

1, 3, 6, 5;

1, 4, 12, 20, 14;

1, 5, 20, 50, 70, 43;

1, 6, 30, 100, 210, 258, 143;

1, 7, 42, 175, 490, 903, 1001, 509;

1, 8, 56, 280, 980, 2408, 4004, 4072, 1922;

1, 9, 72, 420, 1764, 5418, 12012, 18324, 17298, 7651;

1, 10, 90, 600, 2940, 10836, 30030, 61080, 86490, 76510, 31965;