login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
3

%I #7 Jan 27 2024 12:33:04

%S 1,12,97,696,4784,32230,214978,1426566,9441417,62405645,412278981,

%T 2723566163,17996243101,118957645301,786700165122,5205396517853,

%U 34461624895701,228274455988134,1512920531980961,10032446308837778

%N 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.

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

%t a[n_] := SeriesCoefficient[Product[(1-q^(2j-1))/(1-q), {j, 1, n+3}], {q, 0, 2n+6}];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jan 27 2024 *)

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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 12 2007