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A128595 Row sums of triangle A128592. 3
1, 2, 5, 26, 189, 1734, 19305, 253370, 3828825, 65473006, 1249937325, 26352843470, 608142583125, 15247003381854, 412685556908625, 11993673995924378, 372509404162520625, 12313505304343363126, 431620764875678503125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A128592(n,k) is the coefficient of q^(nk+k) in the q-analog of the odd double factorials (2n-1)!!.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = Sum_{k=0..n} { [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) } for n>=0.

PROG

(PARI) {a(n)=sum(k=0, n, polcoeff(prod(j=1, n+1, (1-q^(2*j-1))/(1-q)), (n+1)*k, q))}

CROSSREFS

Cf. A128592; A128080; A001147 ((2n-1)!!); A128593 (column 1), A128594 (column 2).

Sequence in context: A334639 A072268 A019014 * A180749 A323299 A111195

Adjacent sequences:  A128592 A128593 A128594 * A128596 A128597 A128598

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 12 2007

STATUS

approved

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Last modified May 5 19:09 EDT 2021. Contains 343573 sequences. (Running on oeis4.)