A128594 Column 2 of triangle A128592; a(n) = coefficient of q^(2n+6) in the q-analog of the odd double factorials (2n+5)!! for n>=0.

1, 12, 97, 696, 4784, 32230, 214978, 1426566, 9441417, 62405645, 412278981, 2723566163, 17996243101, 118957645301, 786700165122, 5205396517853, 34461624895701, 228274455988134, 1512920531980961, 10032446308837778

Offset: 0

Author

Paul D. Hanna, Mar 12 2007

Keywords

• nonn

Crossrefs

Cf. A128592; A128080; A001147 ((2n-1)!!); A128593 (column 1), A128595 (row sums).

Programs

Mathematica

a[n_] := SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+3}], {q, 0, 2n+6}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 27 2024 *)

PARI

{a(n)=polcoeff(prod(j=1,n+3,(1-q^(2*j-1))/(1-q)),2*n+6,q)}

Formula

a(n) = [q^(2n+6)] Product_{j=1..n+3} (1-q^(2j-1))/(1-q) for n>=0.