A128597 Column 2 of triangle A128596; a(n) = coefficient of q^(2n+4) in the q-analog of the even double factorials (2n+4)!! for n>=0.

1, 7, 46, 297, 1919, 12399, 80241, 520399, 3382588, 22034519, 143826980, 940569228, 6161492611, 40426009162, 265617089899, 1747501590554, 11510584144337, 75901841055650, 501007227527884, 3310076954166501

Offset: 0

Author

Paul D. Hanna, Mar 12 2007

Keywords

• nonn

Crossrefs

Cf. A128596; A128084; A000165 ((2n)!!); A128086 (column 1), A128598 (column 3).

Programs

PARI

{a(n)=polcoeff(prod(j=1,n+2,(1-q^(2*j))/(1-q)),2*n+4,q)}

Formula

a(n) = [q^(2n+4)] Product_{j=1..n+2} (1-q^(2j))/(1-q) for n>=0.