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A117275 Number of partitions of n with no even parts repeated and with no 1's. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A123552 A071610 A198726 * A327725 A253926 A277579

Adjacent sequences:  A117272 A117273 A117274 * A117276 A117277 A117278

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 06 2006

STATUS

approved

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Last modified September 22 15:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)