cp's OEIS Frontend

A118082 Number of partitions of n such that largest part k occurs floor(k/2) times.

%I A118082 #3 Mar 30 2012 17:36:09
%S A118082 1,0,1,2,2,3,3,4,5,6,8,10,12,15,19,22,27,32,39,45,54,63,75,87,102,118,
%T A118082 139,160,186,214,248,284,328,375,430,490,561,637,727,824,935,1058,
%U A118082 1199,1352,1528,1720,1938,2177,2448,2743,3079,3445,3856,4307,4813,5365,5985
%N A118082 Number of partitions of n such that largest part k occurs floor(k/2) times.
%C A118082 Also number of partitions of n such that if the number of parts is k, then the smallest part is floor(k/2). Example: a(8)=5 because we have [7,1],[6,1,1],[5,2,1],[4,3,1] and [2,2,2,2].
%F A118082 G.f.=sum(x^(k*floor(k/2))/product(1-x^j, j=1..k-1), k=1..infinity).
%e A118082 a(8)=5 because we have [4,4],[3,2,2,1],[3,2,1,1,1],[3,1,1,1,1,1] and [2,1,1,1,1,1,1].
%p A118082 g:=sum(x^(k*floor(k/2))/product(1-x^j,j=1..k-1),k=1..15): gser:=series(g,x=0,65): seq(coeff(gser,x,n),n=0..60);
%Y A118082 Cf. A118083, A118084.
%K A118082 nonn
%O A118082 0,4
%A A118082 _Emeric Deutsch_, Apr 12 2006