A128568 Column 1 of triangle A128567.

1, 6, 31, 133, 587, 2531, 10950, 47185, 203704, 879711, 3804530, 16464710, 71312805, 309083291, 1340546867, 5817555402, 25258769216, 109711224970, 476675868834, 2071569641859, 9004430215111, 39144480326143, 170184867215647, 739924236443359, 3217001700174226

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{s=1..n+1} A047812(n+2,s)*A047812(s+1,1) = Sum_{s=1..n+1} A047812(n+2,s)*A007042(s+1) for n >= 0. - Petros Hadjicostas, May 31 2020

Prog

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

Crossrefs

Cf. A007042, A047812, A128567, A128569 (column 2), A128602 (row sums).

Sequence in context: A225425 A267890 A244199 * A079924 A009076 A291396

Adjacent sequences: A128565 A128566 A128567 * A128569 A128570 A128571

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2007

Status

approved