A193444 E.g.f.: exp( Sum_{n>=1} n!*x^(2*n)/(2*n)! ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.

1, 1, 5, 51, 857, 21045, 702597, 30379839, 1642718865, 108171928521, 8495805003525, 782625366185355, 83400601634195049, 10163125433194019325, 1402348965454767334725, 217258436356989650347095, 37513434482581646048138145, 7172552434209226974773867025

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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

Cf. A193441, A193442, A193443, A001813 ((2*n)!/n!).

Sequence in context: A218675 A182316 A077392 * A243242 A111340 A124559

Adjacent sequences: A193441 A193442 A193443 * A193445 A193446 A193447

Keyword

nonn

Author

Paul D. Hanna, Jul 25 2011

Status

approved