A192784 G.f. satisfies: A(x) = Product_{n>=1} (1 + x^n*A(x)^(n^2)).

1, 1, 2, 8, 38, 201, 1164, 7188, 46576, 313823, 2185642, 15668473, 115281167, 868757478, 6696711294, 52757324970, 424590429862, 3490344692094, 29310836035090, 251525003170386, 2206548594680093, 19798923287905907, 181797157100106619

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} -(-1)^(n/d)*d*A(x)^(n*d) ).

Example

G.f: A(x) = 1 + x + 2*x^2 + 8*x^3 + 38*x^4 + 201*x^5 + 1164*x^6 +...
The g.f. A = A(x) satisfies:
A = (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=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, (-1)^(m/d-1)*d*A^(m*d))+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Cf. A192768.

Sequence in context: A369208 A234939 A365751 * A108246 A020031 A179323

Adjacent sequences: A192781 A192782 A192783 * A192785 A192786 A192787

Keyword

nonn

Author

Paul D. Hanna, Jul 09 2011

Status

approved