A134345 Number of partitions of n into odd squarefree parts.

1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 23, 27, 32, 38, 44, 52, 61, 71, 82, 95, 109, 126, 144, 165, 189, 215, 245, 278, 316, 358, 405, 458, 516, 581, 654, 734, 824, 923, 1033, 1155, 1289, 1438, 1602, 1783, 1982, 2202, 2444, 2710, 3002, 3323, 3675, 4061

Offset: 0

Author

Joerg Arndt, Aug 27 2008

Keywords

• nonn

Comments

Also number of partitions into parts m such that 2*m is squarefree.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Joerg Arndt, Matters Computational (The Fxtbook), section 16.4.3 "Partitions into square-free parts", pp.351-352

Programs

PARI

N=75; x='x+O('x^N); Vec( 1/prod(n=1, N, 1-moebius(2*n-1)^2*x^(2*n-1) ) )

Formula

G.f.: 1/prod(n>=1, 1 - moebius(2*n-1)^2 * x^(2*n-1)) = 1/prod(n>=1, 1 - moebius(2*n)^2 * x^(n)).