A227619 G.f.: A(x) = 1+x + Sum_{n>=2} (A(x)^n - 1)^n.

1, 1, 4, 63, 1278, 29764, 758065, 20611793, 590579518, 17707907024, 553879330720, 18066513887790, 615744470668778, 22014659625607877, 830262409494773896, 33243718957578687811, 1422095813097928147636, 65311403344808947050730, 3227884786251446164710376

Offset: 0

Author

Paul D. Hanna, Aug 21 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 63*x^3 + 1278*x^4 + 29764*x^5 +...
where
A(x) = 1+x + (A(x)^2 - 1)^2 + (A(x)^3 - 1)^3 + (A(x)^4 - 1)^4 + (A(x)^5 - 1)^5 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A122400.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+x+sum(k=2,n,(A^k-1 +x*O(x^n))^k));polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))

Formula

a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.9913753087... . - Vaclav Kotesovec, May 07 2014