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%I #12 Mar 07 2016 06:33:59
%S 1,1,2,2,4,4,8,7,14,12,24,19,39,30,62,45,95,67,144,97,212,139,309,195,
%T 442,272,626,373,873,508,1209,684,1653,915,2245,1212,3019,1597,4035,
%U 2087,5348,2714,7051,3506,9229,4508,12022,5763,15565,7338,20063,9296,25722
%N Number of partitions of n with at most 2 odd parts.
%H Alois P. Heinz, <a href="/A100835/b100835.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4))/Product(1-x^(2*i), i=1..infinity). More generally, g.f. for number of partitions of n with at most k odd parts is (1+Sum(x^i/Product(1-x^(2*j), j=1..i), i=1..k))/Product(1-x^(2*i), i=1..infinity).
%e a(5) = 4 because we have [5], [4,1], [3,2] and [2,2,1] (the partitions [3,1,1], [2,1,1,1] and [1,1,1,1,1] do not qualify).
%p g:=(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4))/product(1-x^(2*i), i=1..40): gser:=series(g, x, 60): seq(coeff(gser, x, n), n=0..55); # _Emeric Deutsch_, Feb 16 2006
%t nmax = 50; CoefficientList[Series[(1+x/(1-x^2)+x^2/(1-x^2)/(1-x^4)) * Product[1/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 07 2016 *)
%Y Cf. A000070, A008951, A000097, A000098, A000710.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jan 13 2005
%E More terms from _Emeric Deutsch_, Feb 16 2006
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