cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A117275 Number of partitions of n with no even parts repeated and with no 1's.

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%I A117275 #6 Mar 07 2016 04:57:36
%S A117275 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,
%T A117275 184,220,259,307,364,426,502,590,688,806,941,1093,1272,1478,1710,1980,
%U A117275 2290,2638,3042,3503,4021,4618,5296,6060,6934,7924,9038,10306,11740
%N A117275 Number of partitions of n with no even parts repeated and with no 1's.
%C A117275 Column 0 of A117274.
%F A117275 G.f.: (1+x^2)*product((1+x^(2k))/(1-x^(2k-1)), k=2..infinity).
%F A117275 a(n) ~ exp(sqrt(n/2)*Pi) * Pi / (2^(17/4) * n^(5/4)). - _Vaclav Kotesovec_, Mar 07 2016
%e A117275 a(8)=4 because we have [8],[6,2],[5,3] and [3,3,2].
%p A117275 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);
%t A117275 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 *)
%Y A117275 Cf. A117274.
%K A117275 nonn
%O A117275 0,6
%A A117275 _Emeric Deutsch_, Mar 06 2006