A192783 G.f. satisfies: A(x) = Product_{n>=1} 1/(1 - x^n*A(x)^(n^3)).

1, 1, 3, 16, 119, 1145, 13301, 180464, 2821941, 50400230, 1022250876, 23424407915, 602724515761, 17299947151776, 550101222059396, 19246320555772626, 736247255316380311, 30620337253882961105, 1377609185722013042566, 66750666290443384609574

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

G.f. satisfies: A(x) = exp( Sum_{n>=1} (x^n/n)*Sum_{d|n} d*A(x)^(n*d^2) ).

Example

G.f: A(x) = 1 + x + 3*x^2 + 16*x^3 + 119*x^4 + 1145*x^5 + 13301*x^6 +...
The g.f. A = A(x) satisfies:
A = 1/((1 - x*A)*(1 - x^2*A^8)*(1 - x^3*A^27)*(1 - x^4*A^64)*...),
as well as the logarithmic series:
log(A) = x*A + x^2*(A^2 + 2*A^8)/2 + x^3*(A^3 + 3*A^27)/3 + x^4*(A^4 + 2*A^16 + 4*A^64)/4 + x^5*(A^5 + 5*A^125)/5 + x^6*(A^6 + 2*A^24 + 3*A^54 + 6*A^216)/6  +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, 1-x^k*(A+x*O(x^n))^(k^3))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (x^m/m)*sumdiv(m, d, d*(A+x*O(x^n))^(m*d^2))))); polcoeff(A, n)}

Crossrefs

Cf. A109085, A192768.

Sequence in context: A125807 A125222 A199670 * A136168 A187735 A200318

Adjacent sequences: A192780 A192781 A192782 * A192784 A192785 A192786

Keyword

nonn

Author

Paul D. Hanna, Jul 09 2011

Status

approved