A181445 G.f. satisfies: A(x) = Sum_{n>=0} log(1 + x*A(2^n*x))^n/n!.

1, 1, 2, 10, 110, 2468, 110678, 9893848, 1765620796, 629689184768, 449004143002080, 640244024341490536, 1825757754872909135396, 10412557570967501281794528, 118766811331255795668894586000

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling1(n,k) * A(2^k*x)^n/n!. - Paul D. Hanna, Jan 16 2013

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 110*x^4 + 2468*x^5 +...
A(x) = 1 + log(1+x*A(2*x)) + log(1+x*A(4*x))^2/2! + log(1+x*A(8*x))^3/3! + log(1+x*A(16*x))^4/4! + log(1+x*A(32*x))^5/5! +...

Prog

(PARI) {a(n)=local(A=1+sum(m=1, n-1, a(m)*x^m)); polcoeff(sum(m=0, n, log(1+x*subst(A, x, 2^m*x)+x*O(x^n))^m/m!), 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, 2^k*x+x*O(x^n))^m)*x^m/m!)); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A132695.

Sequence in context: A113147 A335946 A206154 * A231969 A062499 A305854

Adjacent sequences: A181442 A181443 A181444 * A181446 A181447 A181448

Keyword

nonn

Author

Paul D. Hanna, Oct 20 2010

Status

approved