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A092295 Number of partitions of n with even number (or 0) 2's. 5
1, 1, 1, 2, 4, 5, 7, 10, 15, 20, 27, 36, 50, 65, 85, 111, 146, 186, 239, 304, 388, 488, 614, 767, 961, 1191, 1475, 1819, 2243, 2746, 3361, 4096, 4988, 6047, 7322, 8836, 10655, 12801, 15360, 18384, 21978, 26199, 31196, 37062, 43979, 52072, 61579, 72682 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = A000041(n)-a(n-2).

G.f.=1/[(1+x^2)*product(1-x^j, j=1..infinity)]. - Emeric Deutsch, Mar 30 2006

a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)). - Vaclav Kotesovec, Oct 30 2015

EXAMPLE

a(5)=5 because the partitions [5],[4,1],[3,1,1],[2,2,1] and [1,1,1,1,1] of 5 have an even number of 2's ([3,2] and [2,1,1,1] do not qualify).

MAPLE

g:=1/(1+x^2)/product(1-x^j, j=1..70): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..47); # Emeric Deutsch, Mar 30 2006

MATHEMATICA

nmax = 50; CoefficientList[Series[1/((1+x^2) * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *)

CROSSREFS

Cf. A087787.

Sequence in context: A018301 A218074 A241735 * A277102 A168639 A275802

Adjacent sequences:  A092292 A092293 A092294 * A092296 A092297 A092298

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 06 2004

EXTENSIONS

More terms from Benoit Cloitre, Feb 08 2004

STATUS

approved

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Last modified April 4 05:15 EDT 2020. Contains 333212 sequences. (Running on oeis4.)