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A128568 Column 1 of triangle A128567. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 07:09 EST 2021. Contains 340360 sequences. (Running on oeis4.)