A205570 E.g.f.: 1/sqrt(1+x^2 - 2*x*cosh(x)).

1, 1, 2, 9, 60, 485, 4680, 53557, 709968, 10662633, 178786080, 3312164801, 67201649856, 1481949570829, 35291569832064, 902631317654445, 24676916031310080, 718135040275928657, 22164641043514532352, 723163494821506484473, 24869366907327781002240

Offset

0,3

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

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

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 60*x^4/4! + 485*x^5/5! +...

Mathematica

CoefficientList[Series[1/Sqrt[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/sqrt(1+x^2-2*x*cosh(x +x*O(x^n))), n)}

Crossrefs

Cf. A205569.

Sequence in context: A156272 A366240 A363390 * A116364 A354314 A354496

Adjacent sequences: A205567 A205568 A205569 * A205571 A205572 A205573

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2012

Status

approved