A027350 Number of partitions of n into distinct odd parts, the least being 3.

0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 4, 3, 4, 4, 5, 5, 5, 6, 7, 8, 7, 9, 9, 11, 10, 13, 13, 15, 14, 17, 18, 21, 20, 23, 25, 27, 28, 31, 34, 36, 38, 41, 46, 48, 51, 54, 61, 63, 68, 72, 80, 83, 89, 94, 104, 109, 116

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027349.

Programs

PARI

N=99;x='x+O('x^N);
t=sum(n=2,N,x^(n^2-1)/prod(k=1,n-2,1-x^(2*k))); /* == x^3 + x^8 + x^10 + ... */
v=Vec(t) /* show terms for n>=3 */  /* Joerg Arndt, Jan 29 2011 */

Formula

G.f. sum(n>=2, x^(n^2-1)/prod(k=1,n-2,1-x^(2*k))) - Joerg Arndt, Jan 29 2011

a(n) ~ exp(Pi*sqrt(n/6)) / (2^(15/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Oct 09 2018