OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..830
FORMULA
a(n) ~ 2^(4*n - 2) / ((4 - Pi) * n^2). - Vaclav Kotesovec, Oct 05 2019
EXAMPLE
L.g.f.: L(x) = x + 7*x^2/2 + 64*x^3/3 + 667*x^4/4 + 7526*x^5/5 + 89614*x^6/6 +...
such that
exp(L(x)) = 1 + x + 2^2*x^2 + 5^2*x^3 + 14^2*x^4 + 42^2*x^5 + 132^2*x^6 + 429^2*x^7 +...+ A000108(n)^2*x^n +...
G.f: (Pi - 3*E(4*sqrt(x)) + (1-16*x)*K(4*sqrt(x)))/(4*E(4*sqrt(x)) - 2*(1-16*x)*K(4*sqrt(x)) - Pi), where K(x) and E(x) are the complete elliptic integrals of the 1st and 2nd kind. - Vladimir Reshetnikov, Nov 11 2015
MATHEMATICA
Series[(Pi - 3 EllipticE[16 x] + (1 - 16 x) EllipticK[16 x])/(4 EllipticE[16 x] - 2 (1 - 16 x) EllipticK[16 x] - Pi), {x, 0, 20}][[3]] (* Vladimir Reshetnikov, Nov 11 2015 *)
PROG
(PARI) {a(n)=n*polcoeff(log(sum(m=0, n+1, binomial(2*m, m)^2/(m+1)^2*x^m)+x*O(x^n)), n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 13 2012
STATUS
approved