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
Keywords
Examples
a(8)=4 because we have [8],[6,2],[5,3] and [3,3,2].
Crossrefs
Cf. A117274.
Programs
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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);
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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 *)
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
Comments