A128569 Column 2 of triangle A128567.

1, 14, 117, 813, 4871, 27743, 151208, 804065, 4185683, 21472005, 108766010, 545507633, 2712801330, 13394412999, 65722444172, 320721839860, 1557502222385, 7530671086667, 36267851679585, 174038009185816, 832392015517829, 3969017685816667, 18871416851149078

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{s=2..n+2} A047812(n+3,s)*A047812(s+1,2) for n >= 0. - Petros Hadjicostas, May 31 2020

Prog

(PARI) {a(n)=local(M); M=matrix(n+3, n+3, 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)))); (M^2)[n+3, 3]}

Crossrefs

Cf. A047812, A128567, A128568 (column 1), A128602 (row sums).

Sequence in context: A121783 A155647 A279855 * A138431 A175874 A359184

Adjacent sequences: A128566 A128567 A128568 * A128570 A128571 A128572

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2007

Status

approved