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

1, 1, 2, 2, 4, 6, 8, 10, 14, 18, 22, 29, 36, 46, 59, 72, 88, 110, 132, 160, 194, 232, 276, 330, 392, 464, 550, 648, 760, 894, 1044, 1216, 1418, 1644, 1905, 2204, 2540, 2924, 3364, 3859, 4420, 5060, 5778, 6590, 7514, 8544, 9706, 11018, 12484, 14130, 15980

Offset: 1

Author

Emeric Deutsch, Feb 26 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A116858.

Programs

Maple

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);

Formula

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).