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)!!.
FORMULA
a(n) = Sum_{k=0..n} { [q^(nk+k)] Product_{j=1..n+1} (1-q^(2j-1))/(1-q) } for n>=0.
MATHEMATICA
a[n_] := Sum[SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+1}], {q, 0, k(n+1)}], {k, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 27 2024 *)
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 12 2007
STATUS
approved