cp's OEIS Frontend

A116859 Sum of the sizes of the Durfee squares of all partitions of n into distinct parts.

%I A116859 #3 Mar 30 2012 17:36:08
%S A116859 1,1,2,2,4,6,8,10,14,18,22,29,36,46,59,72,88,110,132,160,194,232,276,
%T A116859 330,392,464,550,648,760,894,1044,1216,1418,1644,1905,2204,2540,2924,
%U A116859 3364,3859,4420,5060,5778,6590,7514,8544,9706,11018,12484,14130,15980
%N A116859 Sum of the sizes of the Durfee squares of all partitions of n into distinct parts.
%C A116859 a(n)=Sum(k*A116858(n,k),k>=1).
%F A116859 G.f.=sum(kx^(k(3k-1)/2)*(1+x^(2k))*product((1+x^j)/(1-x^j), j=1..k-1)/(1-x^k), k=1..infinity).
%e A116859 a(8)=10 because the partitions of 8 into distinct parts are [8],[7,1],[6,2],[5,3],[5,2,1] and [4,3,1], the sum of the sizes of their Durfee squares being 1+1+2+2+2+2=10.
%p A116859 f:=sum(k*x^(k*(3*k-1)/2)*(1+x^(2*k))*product((1+x^j)/(1-x^j),j=1..k-1)/(1-x^k),k=1..10): fser:=series(f,x=0,60): seq(coeff(fser,x^n),n=1..55);
%Y A116859 Cf. A116858.
%K A116859 nonn
%O A116859 1,3
%A A116859 _Emeric Deutsch_, Feb 26 2006