0,3

a(n) is the n-th term in the q-analog of odd double factorial (2n+1)!!,

in which the coefficients of q (triangle A128080) begin:

1;

(1);

1,(1),1;

1,2,(3),3,3,2,1;

1,3,6,(9),12,14,15,14,12,9,6,3,1;

1,4,10,19,(31),45,60,74,86,94,97,94,86,74,60,45,31,19,10,4,1;

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

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

Cf. A001147 ((2n-1)!!); A128080 (triangle), A128081 (central terms).

Sequence in context: A127927 A123222 A112566 this_sequence A047012 A120305 A049170

Adjacent sequences: A128079 A128080 A128081 this_sequence A128083 A128084 A128085

nonn

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