A205569 E.g.f.: 1/(1+x^2 - 2*x*cosh(x)).

1, 2, 6, 30, 216, 1930, 20400, 251174, 3541888, 56226258, 991514880, 19230159982, 406873353216, 9326318738906, 230222431688704, 6089006394645750, 171780282479247360, 5149076226504182434, 163421449125050253312, 5474820500060681776574

Offset

0,2

Comments

Radius of convergence of e.g.f. is |x| < r where r = LambertW(1) = exp(-LambertW(1)) = 0.56714329040978...

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(2*n-1) == 2 (mod 4), a(2*n+2) == 0 (mod 4), for n>=1.

a(n) ~ n! * exp(c*n)/((1-c)*(1+c)^2), where c = LambertW(1) = 0.5671432904... - Vaclav Kotesovec, Jun 26 2013

Example

E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 30*x^3/3! + 216*x^4/4! + 1930*x^5/5! +...

Mathematica

CoefficientList[Series[1/(1+x^2 - 2*x*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

Prog

(PARI) {a(n)=n!*polcoeff(1/(1+x^2-2*x*cosh(x +x*O(x^n))), n)}

Crossrefs

Cf. A205570.

Sequence in context: A293756 A161620 A333508 * A108204 A088160 A112317

Adjacent sequences: A205566 A205567 A205568 * A205570 A205571 A205572

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2012

Status

approved