A116859 - OEIS

%I #3 Mar 30 2012 17:36:08

%S 1,1,2,2,4,6,8,10,14,18,22,29,36,46,59,72,88,110,132,160,194,232,276,

%T 330,392,464,550,648,760,894,1044,1216,1418,1644,1905,2204,2540,2924,

%U 3364,3859,4420,5060,5778,6590,7514,8544,9706,11018,12484,14130,15980

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

%C a(n)=Sum(k*A116858(n,k),k>=1).

%F 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 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 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 Cf. A116858.

%K nonn

%O 1,3

%A _Emeric Deutsch_, Feb 26 2006