A221101 E.g.f. satisfies: A(x) = Sum_{n>=0} log(1 + x*A(n*x))^n/n!.

1, 1, 2, 12, 144, 3160, 118380, 7174188, 692356896, 104696597808, 24680489921280, 9010186432576560, 5073501307520289600, 4385657278007399474496, 5797249519065509217375936, 11674185903250032386477342880, 35692663320428574506107140979200

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling1(n,k) * A(k*x)^n/n!.

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 144*x^4/4! + 3160*x^5/5! +...
where
A(x) = 1 + log(1 + x*A(x)) + log(1 + x*A(2*x))^2/2! + log(1 + x*A(3*x))^3/3! + log(1 + x*A(4*x))^4/4! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, log(1+x*subst(A, x, m*x+x*O(x^n)))^m/m!)); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling1(m, k)*subst(A, x, k*x+x*O(x^n))^m)*x^m/m!)); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A189981, A221100.

Sequence in context: A035049 A010790 A321631 * A187748 A324140 A296137

Adjacent sequences: A221098 A221099 A221100 * A221102 A221103 A221104

Keyword

nonn

Author

Paul D. Hanna, Jan 01 2013

Status

approved