OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..150
FORMULA
E.g.f.: 1 / [ Sum_{n>=0} (-1)^n * A063902(n) * x^(2*n) / (2*n)! ].
From Vaclav Kotesovec, Jun 14 2015: (Start)
a(n) ~ c * d^n * n!^2 / sqrt(n), where d = 3*A258895 = 96*Pi / (Gamma(1/6) * Gamma(1/3))^2 = 2^(17/3) * Pi^2 / Gamma(1/3)^6 = 1.3563128975502615865238..., c = 0.8047308283353177558313... = 12/(Gamma(1/3)*Gamma(1/6)) = 2^(7/3)*sqrt(3*Pi) / Gamma(1/3)^3.
a(n) ~ 2^(5*n+3) * 3^(n+1) * Pi^(n+1) * n^(2*n+1/2) / (exp(2*n) * Gamma(1/6)^(2*n+1) * Gamma(1/3)^(2*n+1)).
a(n) ~ sqrt(3) * 2^((17*n+10)/3) * Pi^(2*n+3/2) * n^(2*n+1/2) / (exp(2*n) * Gamma(1/3)^(6*n+3)).
(End)
EXAMPLE
E.g.f.: A(x) = 1 + x^2/2! + 4*x^4/4! + 40*x^6/6! + 760*x^8/8! + 23200*x^10/10! +...
PROG
(PARI) {a(n) = local(A=1+x); for(i=1, n, A = exp( intformal( A * intformal(1/A^2 + x*O(x^n)) ) ) ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(2*n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 06 2015
STATUS
approved