A144014 E.g.f. satisfies: A'(x) = 1 + x*A(x)^4 where A(0) = 1.

1, 1, 1, 8, 48, 368, 3900, 46992, 647472, 10294848, 182582424, 3576144000, 76958290464, 1801577086848, 45572841133248, 1239448991058432, 36058780518552000, 1117339391835583488, 36741513671695717632

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..312

Formula

E.g.f. satisfies: A(x) = 1 + Integral [1 + x*A(x)^4] dx.

a(n) ~ n^(n-1/6) * sqrt(2*Pi) / (3^(1/3) * GAMMA(1/3) * exp(n) * r^(n+2/3)), where r = 0.52731343741213... (multiplicative constant is conjectured, holds 14 decimal places). - Vaclav Kotesovec, Feb 24 2014

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 8*x^3/3! + 48*x^4/4! + 368*x^5/5! +...
A(x)^4 = 1 + 4*x + 16*x^2/2! + 92*x^3/3! + 780*x^4/4! + 7832*x^5/5! +...
x*A(x)^4 = x + 8*x^2/2! + 48*x^3/3! + 368*x^4/4! + 3900*x^5/5! +...
A'(x) = 1 + x + 8*x^2/2! + 48*x^3/3! + 368*x^4/4! + 3900*x^5/5! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1+x*(A+x*O(x^n))^4)); n!*polcoeff(A, n)}

Crossrefs

Cf. A144012, A144013.

Sequence in context: A215706 A200161 A172111 * A131681 A077708 A165041

Adjacent sequences: A144011 A144012 A144013 * A144015 A144016 A144017

Keyword

nonn

Author

Paul D. Hanna, Sep 10 2008

Status

approved