0,4

a(n) is the central term of the q-analog of odd double factorials,

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

n=0: (1);

n=1: (1);

n=2: 1,(1),1;

n=3: 1,2,3,(3),3,2,1;

n=4: 1,3,6,9,12,14,(15),14,12,9,6,3,1;

n=5: 1,4,10,19,31,45,60,74,86,94,(97),94,86,74,60,45,31,19,10,4,1;

n=6: 1,5,15,34,65,110,170,244,330,424,521,614,696,760,801,(815),...;

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))/(1-q)), n*(n-1)/2, q))

Cf. A001147 ((2n-1)!!); A128080 (triangle), A128082 (diagonal).

Sequence in context: A060148 A143435 A132437 this_sequence A046635 A140286 A091713

Adjacent sequences: A128078 A128079 A128080 this_sequence A128082 A128083 A128084

nonn

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