A129275 Column 1 of triangle A129274; a(n) is the coefficient of q^(n+2) in the squared q-factorial of n+2.

1, 10, 71, 474, 3103, 20190, 131204, 853176, 5555674, 36237258, 236763125, 1549496420, 10156512792, 66669881442, 438226458380, 2884072387268, 19002479773355, 125335000366692, 827479642104143, 5468060901435850

Offset: 0

Author

Paul D. Hanna, Apr 07 2007

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..300
• Eric Weisstein's World of Mathematics, q-Factorial.

Crossrefs

Cf. A129274.

Programs

Maple

P:= (1+q)^2: A[0]:= 1:
for n from 1 to 50 do
  P:= normal(P * (1-q^(n+2))^2/(1-q)^2);
  A[n]:= coeff(P,q,n+2);
od:
seq(A[i],i=0..50); # Robert Israel, Jun 25 2018

PARI

a(n)=polcoeff(prod(i=1,n+2,(1-x^i)/(1-x))^2,n+2)

Formula

a(n) = [q^(n+2)] Product_{i=1..n+2} { (1-q^i)/(1-q) }^2.