A128602 - OEIS

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

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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