A192768 G.f. satisfies: A(x) = Product_{n>=1} 1/(1 - x^n*A(x)^(n^2)).

1, 1, 3, 12, 59, 328, 1987, 12819, 86840, 611993, 4458355, 33425634, 257101218, 2024379762, 16292282944, 133886553125, 1122781620139, 9605824882455, 83838618087996, 746620718694421, 6786473727400695, 62988617523112588, 597257517555481856

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 59*x^4 + 328*x^5 + 1987*x^6 +...
The g.f. A = A(x) satisfies the product:
A = 1/((1 - x*A)*(1 - x^2*A^4)*(1 - x^3*A^9)*(1 - x^4*A^16)*...)
as well as the logarithmic series:
log(A) = x*A + x^2*(A^2 + 2*A^4)/2 + x^3*(A^3 + 3*A^9)/3 + x^4*(A^4 + 2*A^8 + 4*A^16)/4 + x^5*(A^5 + 5*A^25)/5 + x^6*(A^6 + 2*A^12 + 3*A^18 + 6*A^36)/6 +...

Prog

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

Crossrefs

Cf. A192783, A192784.

Sequence in context: A181328 A058861 A105668 * A179325 A064856 A080337

Adjacent sequences: A192765 A192766 A192767 * A192769 A192770 A192771

Keyword

nonn

Author

Paul D. Hanna, Jul 09 2011

Status

approved