OFFSET
0,3
FORMULA
G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 12*k + 41)*k/6].
EXAMPLE
Equals the number of subpartitions of the partition:
{(k^2 + 12*k + 41)*k/6, k>=0} = [0,9,23,43,70,105,149,203,268,345,...]
as illustrated by g.f.:
1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^9 + 10*x^2*(1-x)^23 + 195*x^3*(1-x)^43 + 5940*x^4*(1-x)^70 + 257300*x^5*(1-x)^105 + 14989472*x^6*(1-x)^149 + 1130000385*x^7*(1-x)^203 ...
PROG
(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+12*k+41)*k/6)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 27 2006
STATUS
approved