A233536 E.g.f. satisfies: A(x) = exp( Integral (1 + x*A(x) + x^2*A(x)^2)/A(x) dx ).

1, 1, 1, 4, 15, 64, 355, 2424, 17521, 145280, 1360521, 13884320, 153669791, 1856114688, 24118429595, 335060591488, 4969674145185, 78372603670528, 1307723372124625, 23033289496343040, 427152897455369455, 8316956600840806400, 169633856906699985555, 3617390574964855445504, 80494223066221543513745

Offset

0,4

Comments

Compare to: G(x) = exp( Integral (1 + 2*x*G(x) + x^2*G(x)^2)/G(x) dx ) holds when G(x) = 1/(1-x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

E.g.f. satisfies: A'(x) = (1 - x^3*A(x)^3) / (1 - x*A(x)).

a(n) ~ n! * d^(n+3), where d = 0.9271503577507272... - Vaclav Kotesovec, Feb 24 2014

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 15*x^4/4! + 64*x^5/5! + 355*x^6/6! +...
Related expansions:
A'(x) = 1 + x*A(x) + x^2*A(x)^2 = 1 + x + 4*x^2/2! + 15*x^3/3! + 64*x^4/4! + 355*x^5/5! + 2424*x^6/6! + 17521*x^7/7! +...
(1 + x*A(x) + x^2*A(x)^2)/A(x) = 1 + 3*x^2/2! + 2*x^3/3! + 23*x^4/4! + 36*x^5/5! + 673*x^6/6! + 1328*x^7/7! +...
log(A(x)) = x + 3*x^3/3! + 2*x^4/4! + 23*x^5/5! + 36*x^6/6! + 673*x^7/7! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(intformal((1+x*A+x^2*A^2)/A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A323789 A341922 A007526 * A349202 A318121 A357785

Adjacent sequences: A233533 A233534 A233535 * A233537 A233538 A233539

Keyword

nonn

Author

Paul D. Hanna, Dec 14 2013

Status

approved