A192769 G.f. satisfies: A(x) = exp( Sum_{n>=} (x^n/n)*[Sum_{d|n} d*A(x)^d]^n ).

1, 1, 6, 48, 977, 13378, 680739, 16253410, 638406407, 21983092893, 992808221997, 42510501798854, 20888455486970142, 1827747975355320051, 96671149737735542775, 4002066332008089249033, 193076352317855172664077, 13301772601630930169228482

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Example

G.f.: A(x) = 1 + x + 6*x^2 + 48*x^3 + 977*x^4 + 13378*x^5 +...
The g.f. A = A(x) satisfies:
log(A) = x*A + x^2*(A + 2*A^2)^2/2 + x^3*(A + 3*A^3)^3/3 + x^4*(A + 2*A^2 + 4*A^4)^4/4 + x^5*(A + 5*A^5)^5/5 + x^6*(A + 2*A^2 + 3*A^3 + 6*A^6)^6/6 +...

Prog

(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^d)^m+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Sequence in context: A052744 A267620 A275334 * A324461 A084259 A028308

Adjacent sequences: A192766 A192767 A192768 * A192770 A192771 A192772

Keyword

nonn

Author

Paul D. Hanna, Jul 09 2011

Status

approved