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

Author

Paul D. Hanna, Feb 14 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

PARI

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