OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * k! * a(n-k). - Ilya Gutkovskiy, Jan 27 2020
EXAMPLE
E.g.f.: A(x) = 1 + x^2/2! + 5*x^4/4! + 51*x^6/6! + 857*x^8/8! + 21045*x^10/10! + 702597*x^12/12! +...+ a(n)*x^n/(2*n)! +...
where
log(A(x)) = x^2/2! + 2!*x^4/4! + 3!*x^6/6! + 4!*x^8/8! + 5!*x^10/10! +...
PROG
(PARI) {a(n)=(2*n)!*polcoeff(exp(sum(m=1, n, m!*x^(2*m)/(2*m)!)+O(x^(2*n+1))), 2*n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 25 2011
STATUS
approved