A131310 O.g.f. A(x) satisfies: [x^n] exp(x*A(x)) = [x^n] A(x) / n!.

1, 1, 3, 25, 697, 87261, 63362851, 319794398533, 12896670350677905, 4680059818474453354777, 16983047870459137946598471811, 677909112049327323648624151866814641

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(n+1) = n!*Sum_{k=0..n} (k+1)/(n-k)!*a(k)*a(n-k). - Vladeta Jovovic, Jul 08 2008

Example

O.g.f.: A(x) = 1 + x + 3*x^2 + 25*x^3 + 697*x^4 + 87261*x^5 + 63362851*x^6 +...
exp(x*A(x)) = 1 + x + 3*x^2/2! + 25*x^3/3! + 697*x^4/4! + 87261*x^5/5! + 63362851*x^6/6! +...

Prog

(PARI) {a(n)=local(E=1+x+x*O(x^n), F); for(j=0, n, F=exp(x*E); E=sum(i=0, n, polcoeff(F, i)*i!*x^i)); polcoeff(E, n)}

Crossrefs

Sequence in context: A248417 A355123 A306795 * A362657 A365359 A062411

Adjacent sequences: A131307 A131308 A131309 * A131311 A131312 A131313

Keyword

nonn

Author

Paul D. Hanna, Jun 27 2007

Status

approved