A102230 - OEIS

A102230

Triangle, read by rows, where each column equals the convolution of A032349 with the prior column, starting with column 0 equal to A032349 shift right.

1, 1, 1, 4, 5, 1, 24, 32, 9, 1, 172, 236, 76, 13, 1, 1360, 1896, 656, 136, 17, 1, 11444, 16116, 5828, 1348, 212, 21, 1, 100520, 142544, 53112, 13184, 2376, 304, 25, 1, 911068, 1298524, 494364, 128924, 25436, 3804, 412, 29, 1, 8457504, 12100952

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OFFSET

0,4

COMMENTS

Row sums equal A027307; the self-convolution of the row sums form A032349. Column 0 equals A032349 shift right. Column 1 is A102231. This triangle is a variant of A100326.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

G.f.: A(x, y) = (1+x*F(x))/(1-x*y*F(x)) where F(x) is the g.f. of A032349 and satisfies F(x) = (1+x*F(x))^2/(1-x*F(x))^2.

EXAMPLE

This triangle is generated by the recurrence:

T(n,k) = Sum_{i=0..n-k} T(i+1,0)*T(n-i-1,k-1) for n>k>0,

T(n,0) = Sum_{i=0..n-1} (2*i+1)*T(n-1,i) for n>0, with T(0,0)=1.

Rows begin:

[1],

[1,1],

[4,5,1],