A117275 Number of partitions of n with no even parts repeated and with no 1's.

1, 0, 1, 1, 1, 2, 3, 3, 4, 6, 7, 9, 12, 14, 18, 23, 27, 34, 42, 50, 62, 75, 89, 108, 130, 154, 184, 220, 259, 307, 364, 426, 502, 590, 688, 806, 941, 1093, 1272, 1478, 1710, 1980, 2290, 2638, 3042, 3503, 4021, 4618, 5296, 6060, 6934, 7924, 9038, 10306, 11740

Offset

0,6

Comments

Column 0 of A117274.

Links

Table of n, a(n) for n=0..54.

Formula

G.f.: (1+x^2)*product((1+x^(2k))/(1-x^(2k-1)), k=2..infinity).

a(n) ~ exp(sqrt(n/2)*Pi) * Pi / (2^(17/4) * n^(5/4)). - Vaclav Kotesovec, Mar 07 2016

Example

a(8)=4 because we have [8],[6,2],[5,3] and [3,3,2].

Maple

g:=(1+x^2)*product((1+x^(2*k))/(1-x^(2*k-1)), k=2..53): gser:=series(g, x=0, 62): seq(coeff(gser, x, n), n=0..58);

Mathematica

nmax = 60; CoefficientList[Series[(1-x) * Product[(1+x^(2*k))/(1-x^(2*k-1)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)

Crossrefs

Cf. A117274.

Sequence in context: A071610 A358993 A198726 * A327725 A253926 A277579

Adjacent sequences: A117272 A117273 A117274 * A117276 A117277 A117278

Keyword

nonn

Author

Emeric Deutsch, Mar 06 2006

Status

approved