cp's OEIS Frontend

A092295 Number of partitions of n with even number (or 0) 2's.

%I A092295 #16 Oct 30 2015 11:24:49
%S A092295 1,1,1,2,4,5,7,10,15,20,27,36,50,65,85,111,146,186,239,304,388,488,
%T A092295 614,767,961,1191,1475,1819,2243,2746,3361,4096,4988,6047,7322,8836,
%U A092295 10655,12801,15360,18384,21978,26199,31196,37062,43979,52072,61579,72682
%N A092295 Number of partitions of n with even number (or 0) 2's.
%H A092295 Vaclav Kotesovec, <a href="/A092295/b092295.txt">Table of n, a(n) for n = 0..10000</a>
%F A092295 a(n) = A000041(n)-a(n-2).
%F A092295 G.f.=1/[(1+x^2)*product(1-x^j, j=1..infinity)]. - _Emeric Deutsch_, Mar 30 2006
%F A092295 a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)). - _Vaclav Kotesovec_, Oct 30 2015
%e A092295 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).
%p A092295 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
%t A092295 nmax = 50; CoefficientList[Series[1/((1+x^2) * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 30 2015 *)
%Y A092295 Cf. A087787.
%K A092295 easy,nonn
%O A092295 0,4
%A A092295 _Vladeta Jovovic_, Feb 06 2004
%E A092295 More terms from _Benoit Cloitre_, Feb 08 2004