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

0,4

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

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)).

Prog

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

Crossrefs

Sequence in context: A029014 A304631 A298603 * A112193 A014215 A067014

Adjacent sequences: A134342 A134343 A134344 * A134346 A134347 A134348

Keyword

nonn

Author

Joerg Arndt, Aug 27 2008

Status

approved