A181536 G.f.: A(x) = x*exp( Sum_{n>=1} A(2^(n^2)*x^n)/n ).

1, 2, 18, 348, 22998, 7497180, 11948631604, 81974855239480, 2326992693663022694, 269846257532329078280364, 127041922315653022761148802396, 241938253359964848636177506896485640

Offset

1,2

Comments

Compare g.f. to that of A000081 (number of rooted trees with n nodes):

* G(x) = x*exp( Sum_{n>=1} G(x^n)/n ).

Links

Table of n, a(n) for n=1..12.

Example

G.f.: A(x) = 1 + 2*x + 18*x^2 + 348*x^3 + 22998*x^4 + 7497180*x^5 +...
A(x) = x*exp(A(2*x) + A(2^4*x^2)/2 + A(2^9*x^3)/3 + A(2^16*x^4)/4 +...).

Prog

(PARI) {a(n)=local(A=x+2*x^2); for(i=1, n, A=x*exp(sum(m=1, n, subst(A, x, 2^(m^2)*x^m+x*O(x^n))/m))); polcoeff(A, n)}

Crossrefs

Cf. A181535.

Sequence in context: A090307 A123311 A349881 * A132911 A291902 A336217

Adjacent sequences: A181533 A181534 A181535 * A181537 A181538 A181539

Keyword

nonn

Author

Paul D. Hanna, Oct 30 2010

Status

approved