

A128569


Column 2 of triangle A128567.


3



1, 14, 117, 813, 4871, 27743, 151208, 804065, 4185683, 21472005, 108766010, 545507633, 2712801330, 13394412999, 65722444172, 320721839860, 1557502222385, 7530671086667, 36267851679585, 174038009185816, 832392015517829, 3969017685816667, 18871416851149078
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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, 1q^j)/prod(j=1, r, 1q^j), (r+1)*(c1), q)))); (M^2)[n+3, 3]}


CROSSREFS

Cf. A047812, A128567, A128568 (column 1), A128602 (row sums).
Sequence in context: A121783 A155647 A279855 * A138431 A175874 A006223
Adjacent sequences: A128566 A128567 A128568 * A128570 A128571 A128572


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Mar 12 2007


STATUS

approved



