A180721 L.g.f: A(x) = Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} E( a(n)*x )^n*x^n/n where E(x) = exp(A(x)) is the g.f. of A180720.

1, 3, 16, 183, 6236, 1057176, 1733913028, 74017764628367, 352900886016894052282, 1553933222263165003400252699258, 133132594387470620595913152570240200262971699

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Example

L.g.f: A(x) = x + 3*x^2/2 + 16*x^3/3 + 183*x^4/4 + 6236*x^5/5 +...+ a(n)*x^n/n +...
which also equals the series:
A(x) = log(E(x)) = E(x)*x + E(3*x)^2*x^2/2 + E(16*x)^3*x^3/3 + E(183*x)^4*x^4/4 + E(6236*x)^5*x^5/5 +...+ E(a(n)*x)^n*x^n/n +...
where E(x) is the integer series:
E(x) = 1 + x + 2*x^2 + 7*x^3 + 53*x^4 + 1305*x^5 + 177559*x^6 + 247880897*x^7 + 9252468642944*x^8 +...+ A180720(n)*x^n +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n), L); for(i=1, n, L=Vec(deriv(log(A))); A=exp(sum(m=1, #L, subst(A, x, L[m]*x)^m*x^m/m)+x*O(x^n))); if(n<1, 0, L[n])}

Crossrefs

Cf. A180720.

Sequence in context: A024041 A152554 A254430 * A192668 A045990 A007006

Adjacent sequences: A180718 A180719 A180720 * A180722 A180723 A180724

Keyword

nonn

Author

Paul D. Hanna, Sep 19 2010

Status

approved