OFFSET
1,3
COMMENTS
a(n)=Sum(k*A116858(n,k),k>=1).
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).
EXAMPLE
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.
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 26 2006
STATUS
approved