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A205569 E.g.f.: 1/(1+x^2 - 2*x*cosh(x)). 2
1, 2, 6, 30, 216, 1930, 20400, 251174, 3541888, 56226258, 991514880, 19230159982, 406873353216, 9326318738906, 230222431688704, 6089006394645750, 171780282479247360, 5149076226504182434, 163421449125050253312, 5474820500060681776574 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Radius of convergence of e.g.f. is |x| < r where r = LambertW(1) = exp(-LambertW(1)) = 0.56714329040978...
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 28 2012
STATUS
approved

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Last modified June 18 01:52 EDT 2024. Contains 373468 sequences. (Running on oeis4.)