A027189 Number of partitions of n into an odd number of parts, the least being 3; also, a(n+3) = number of partitions of n into an even number of parts, each >=3.

0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 12, 17, 19, 25, 29, 37, 43, 56, 64, 80, 94, 116, 135, 167, 194, 236, 276, 332, 387, 466, 541, 645, 752, 891, 1034, 1223, 1417, 1666, 1931, 2260, 2613, 3054, 3522, 4098, 4725, 5480

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027195.

Formula

a(n) ~ Pi^2 * exp(Pi*sqrt(2*n/3)) / (8 * 3^(3/2) * n^2). - Vaclav Kotesovec, May 17 2020

G.f.: x^3 * Sum_{k>=0} x^(6*k)/Product_{j=1..2*k} (1-x^j). - Seiichi Manyama, May 15 2023