A229559 E.g.f. A(x) satisfies: A'(x) = A(x) - A(x)^2 + A(x)^3.

1, 1, 2, 8, 46, 340, 3080, 33020, 408760, 5737600, 90041480, 1562155760, 29688699040, 613378208080, 13687826477600, 328103392918400, 8407745335871200, 229363476365320000, 6636554484183747200, 203007064284501963200, 6545704564601880726400, 221887453210925123353600

Offset: 0

Author

Paul D. Hanna, Dec 18 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 46*x^4/4! + 340*x^5/5! +...
where A(x)^2 = 1 + 2*x + 6*x^2/2! + 28*x^3/3! + 180*x^4/4! + 1460*x^5/5! +...
also, A(x)^3 = 1 + 3*x + 12*x^2/2! + 66*x^3/3! + 474*x^4/4! + 4200*x^5/5! +...
and log(A(x)) = x + x^2/2! + 4*x^3/3! + 20*x^4/4! + 134*x^5/5! + 1120*x^6/6! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A124212.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=1+intformal(A-A^2+A^3+x*O(x^n))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Formula

E.g.f. A(x) satisfies: A(x) = exp(x + Integral A(x)^2 - A(x) dx).

a(n) ~ n^n * 3^(3*n/2+3/4) / (exp(n) * Pi^(n+1/2)). - Vaclav Kotesovec, Dec 19 2013