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

1,5

Links

Table of n, a(n) for n=1..62.

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

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 *)

Crossrefs

Cf. A000700.

Sequence in context: A106244 A029023 A140952 * A143752 A145933 A300788

Adjacent sequences: A096908 A096909 A096910 * A096912 A096913 A096914

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 17 2004

Extensions

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

Status

approved