OFFSET
0,2
COMMENTS
The e.g.f. A(x) of this sequence also satisfies:
A(x*y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ] / G(x,y)^N
where
G(x,y) = Limit_{N->oo} [ Sum_{n>=0} (N + n*y)^(4*n) * (x/N^3)^n/n! ]^(1/N)
for all real y.
EXAMPLE
E.g.f.: A(x) = 1 + 4*x + 100*x^2/2! + 4464*x^3/3! + 286816*x^4/4! + 24053120*x^5/5! + 2488967136*x^6/6! + 306383969920*x^7/7! + 43726697867008*x^8/8! + 7098711727021056*x^9/9! + 1291743506952832000*x^10/10! +...
such that
A(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ] / F(x)^N
where
F(x) = Limit_{N->oo} [ Sum_{n>=0} (N + n)^(4*n) * (x/N^3)^n/n! ]^(1/N)
and
F(x) = 1 + x + 9*x^2/2! + 205*x^3/3! + 8033*x^4/4! + 456561*x^5/5! + 34307545*x^6/6! + 3219222301*x^7/7! + 363018204225*x^8/8! + 47866764942721*x^9/9! + 7230829461286121*x^10/10! +...+ A266483(n)*x^n/n! +...
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 30 2015
STATUS
approved