A143925 E.g.f. A(x) satisfies A(x) = exp(x + x^2*A'(x)).

1, 1, 3, 25, 397, 10061, 369061, 18415825, 1197307161, 98248658905, 9928361978281, 1211474323983221, 175635827999270629, 29845580180227776277, 5876070628821158239293, 1327055145216772464211321, 340793190982323564066166321, 98752652958563191504390390577

Offset: 0

Author

Paul D. Hanna, Sep 06 2008

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A386505, A386506, A386507, A386508, A386509.

Cf. A386510, A386511, A386512, A386513.

Cf. A156326.

Programs

PARI

{a(n)=local(A=1+x);for(i=0,n,A=exp(x+x^2*deriv(A)+x*O(x^n)));n!*polcoeff(A,n)}

Formula

a(n) ~ c * (n!)^2, where c = 0.80799863989712622039... - Vaclav Kotesovec, Feb 22 2014

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k * binomial(n-1,k) * a(k) * a(n-1-k). - Seiichi Manyama, Jul 24 2025