0,3

See A128082 for a diagonal of the triangle A128080 of coefficients of q in the q-analog of the odd double factorials.

a(n) is the n-th term in the q-analog of even double factorial (2n)!!,

in which the coefficients of q (triangle A128084) begin:

(1);

1,(1);

1,2,(2),2,1;

1,3,5,(7),8,8,7,5,3,1;

1,4,9,16,(24),32,39,44,46,44,39,32,24,16,9,4,1;

1,5,14,30,54,(86),125,169,215,259,297,325,340,340,325,297,...;

The terms enclosed in parenthesis are initial terms of this sequence.

(PARI) a(n)=if(n==0, 1, polcoeff(prod(k=1, n, (1-q^(2*k))/(1-q)), n, q))

Cf. A000165 ((2n)!!); A128084 (triangle), A128085 (central terms).

Adjacent sequences: A128083 A128084 A128085 this_sequence A128087 A128088 A128089

Sequence in context: A053368 A141753 A014300 this_sequence A131824 A104625 A122446

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Feb 14 2007