A128598 Column 3 of triangle A128596; a(n) = coefficient of q^(3n+9) in the q-analog of the even double factorials (2n+6)!! for n>=0.

1, 24, 297, 3210, 32510, 318171, 3054100, 28980565, 273077443, 2562036673, 23973009386, 223949654108, 2090070431683, 19496003736658, 181815760387221, 1695523268254637, 15813185728272754, 147508341317700463

Offset: 0

Author

Paul D. Hanna, Mar 12 2007

Keywords

• nonn

Crossrefs

Cf. A128596; A128084; A000165 ((2n)!!); A128086 (column 1), A128597 (column 2).

Programs

PARI

{a(n)=polcoeff(prod(j=1,n+3,(1-q^(2*j))/(1-q)),3*n+9,q)}

Formula

a(n) = [q^(3n+9)] Product_{j=1..n+3} (1-q^(2j))/(1-q) for n>=0.