The On-Line Encyclopedia of Integer Sequences (OEIS)

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A117275

Number of partitions of n with no even parts repeated and with no 1's.
(history; published version)

#6 by Vaclav Kotesovec at Mon Mar 07 04:57:36 EST 2016

STATUS

editing

approved

#5 by Vaclav Kotesovec at Mon Mar 07 04:57:27 EST 2016

FORMULA

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

#4 by Vaclav Kotesovec at Mon Mar 07 04:54:35 EST 2016

FORMULA

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

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 *)

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 17:36:09 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Mar 06 2006

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173

#2 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

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

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

NAME

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

DATA

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.

FORMULA

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

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);

CROSSREFS

Cf. A117274.

KEYWORD

nonn

AUTHOR

Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 06 2006

STATUS

approved