OFFSET
0,3
COMMENTS
Sum_{n>=0} a(n)/(2*n)! = 2.
FORMULA
E.g.f.: sqrt(1-x^2)*exp(x*atanh(x)). - Vladimir Kruchinin, Feb 26 2015
EXAMPLE
E.g.f.: A(x) = 1 + x^2/2! + 5*x^4/4! + 69*x^6/6! + 2057*x^8/8! +... where log(A(x)) = x^2/(1*2) + x^4/(3*4) + x^6/(5*6) + x^8/(7*8) +...
MATHEMATICA
nmax = 20; CoefficientList[Series[(1 - Sqrt[x])^((1 - Sqrt[x])/2) * (1 + Sqrt[x])^((1 + Sqrt[x])/2), {x, 0, nmax}], x] * (2*Range[0, nmax])! (* Vaclav Kotesovec, Oct 28 2024 *)
PROG
(PARI) {a(n)=(2*n)!*polcoeff(exp(sum(m=1, n, x^(2*m)/(2*m*(2*m-1)))+x*O(x^(2*n))), 2*n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 08 2013
STATUS
approved