A116928 Number of 1's in all self-conjugate partitions of n.

1, 0, 1, 0, 2, 1, 3, 2, 4, 4, 6, 6, 8, 9, 11, 12, 15, 17, 20, 22, 26, 29, 34, 37, 43, 48, 55, 60, 69, 76, 86, 94, 106, 117, 131, 143, 160, 176, 195, 213, 236, 259, 285, 311, 342, 374, 410, 446, 488, 533, 581, 631, 688, 748, 813, 881, 957, 1038, 1125, 1216, 1317, 1425

Offset: 1

Author

Emeric Deutsch, Feb 26 2006

Keywords

• nonn

Comments

a(n)=Sum(k*A116927(n,k), k>=0).

Examples

			a(12)=6 because the self-conjugate partitions of 12 are [6,2,1,1,1,1],[5,3,2,1,1] and [4,4,2,2], containing a total of six 1's.
		

Crossrefs

Cf. A116927.

Programs

Maple

f:=x+sum(x^(k^2+2)/(1-x^2)/product(1-x^(2*j),j=1..k),k=1..10): fser:=series(f,x=0,70): seq(coeff(fser,x^n),n=1..67);

Formula

G.f.=x+sum(x^(k^2+2)/(1-x^2)/product(1-x^(2j), j=1..k), k=1..infinity).

a(n) = A096911(n)-(1+(-1)^n)/2, m>1. - Vladeta Jovovic, Feb 27 2006