A193197 G.f.: A(x) = Sum_{n>=0} x^(n^2) / Product_{k=1..n} (1 - x^k)^n.

1, 1, 1, 1, 2, 3, 6, 9, 15, 22, 34, 50, 78, 119, 188, 295, 466, 728, 1134, 1742, 2659, 4018, 6037, 9018, 13443, 19993, 29749, 44274, 65976, 98372, 146781, 218922, 326290, 485476, 720817, 1067293, 1575713, 2318852, 3401845, 4975174, 7255629, 10553845, 15317091

Offset

0,5

Links

Table of n, a(n) for n=0..42.

Example

 G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 6*x^6 + 9*x^7 +...
where:
A(x) = 1 + x/(1-x) + x^4/((1-x)*(1-x^2))^2 + x^9/((1-x)*(1-x^2)*(1-x^3))^3 + x^16/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))^4 +...

Prog

 (PARI) {a(n)=local(A=1); polcoeff(sum(m=0, n, x^(m^2)/prod(k=1, m, 1-x^k +x*O(x^n))^m), n)}

Crossrefs

Sequence in context: A086642 A308930 A304620 * A308995 A326470 A326595

Adjacent sequences: A193194 A193195 A193196 * A193198 A193199 A193200

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2011

Status

approved