A128086 A diagonal of the triangle A128084 of coefficients of q in the q-analog of the even double factorials: a(n) = A128084(n,n).

1, 1, 2, 7, 24, 86, 315, 1170, 4389, 16588, 63064, 240901, 923858, 3554747, 13716315, 53054703, 205651975, 798645126, 3106669575, 12102626404, 47210910670, 184385864445, 720920510115, 2821499709615, 11052719207369, 43333403693711

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..25.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A053368 A141753 A014300 * A131824 A256938 A150389

Adjacent sequences: A128083 A128084 A128085 * A128087 A128088 A128089

Keyword

nonn

Author

Paul D. Hanna, Feb 14 2007

Status

approved