A096911 Number of partitions of n into distinct parts with exactly one even part.

0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 18, 20, 23, 26, 30, 34, 38, 43, 49, 55, 61, 69, 77, 86, 95, 106, 118, 131, 144, 160, 177, 195, 214, 236, 260, 285, 312, 342, 375, 410, 447, 488, 534, 581, 632, 688, 749, 813, 882, 957, 1039, 1125, 1217, 1317, 1426

Offset: 1

Author

Vladeta Jovovic, Aug 17 2004

Keywords

• easy
• nonn

Crossrefs

Cf. A000700.

Programs

Mathematica

Drop[ CoefficientList[ Series[x^2/(1 - x^2) * Product[1 + x^(2*i + 1), {i, 0, 70}], {x, 0, 62}], x], 1] (* Robert G. Wilson v, Aug 21 2004 *)

Formula

G.f.: x^2/(1-x^2)*Product(1+x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n into distinct parts with exactly k even parts is x^(k*(k+1))/Product(1-x^(2*i), i=1..k)*Product(1+x^(2*i+1), i=0..infinity).

a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/6)) / (2^(5/4) * Pi * n^(1/4)). - Vaclav Kotesovec, May 29 2018

Extensions

More terms from Robert G. Wilson v, Aug 21 2004