A128602 Row sums of triangle A128567.

1, 3, 12, 60, 315, 1869, 11472, 74797, 502908, 3505031, 24973089, 182208083, 1352620790, 10207771213, 78082422354, 604699597868, 4733082767467, 37406134058641, 298165102770381, 2395219866441531, 19376637845028027, 157757577529194488, 1291926016200778464

Offset

1,2

Comments

A128567 is the matrix square of Parker's partition triangle A047812.

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = Sum_{s=0..n-1} A047812(n,s)*A000108(s+1) for n >= 1. - Petros Hadjicostas, May 31 2020

Prog

(PARI) {a(n)=local(M); M=matrix(n+1, n+1, r, c, if(r<c, 0, if(r==0, 1, polcoeff(prod(j=r+1, 2*r, 1-q^j)/prod(j=1, r, 1-q^j), (r+1)*(c-1), q)))); sum(k=0, n, (M^2)[n+1, k+1])}
/* To display results because the offset was changed: */
vector(28, n, a(n-1)) \\ Petros Hadjicostas, May 31 2020

Crossrefs

Cf. A000108, A047812, A128567, A128568 (column 1), A128569 (column 2).

Sequence in context: A073996 A003483 A278395 * A092803 A181282 A020052

Adjacent sequences: A128599 A128600 A128601 * A128603 A128604 A128605

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2007

Extensions

Offset changed by Petros Hadjicostas, May 31 2020 to agree with A128567

Status

approved