A185071 - OEIS

A185071

E.g.f.: 1/sqrt(cos(x)*cosh(x) - sin(x)*sinh(x)), omitting the zero-valued coefficients of odd powers of x.

1, 1, 11, 311, 17401, 1605121, 221150291, 42544269431, 10895006389681, 3583312720242241, 1472043913711636571, 738696511605374082551, 444643435445854346001961, 316205489853515802822759361, 262279609103378710090568706851, 250969078703002751430687050751671

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OFFSET

0,3

COMMENTS

a(n) == 1 (mod 10).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

FORMULA

a(n) ~ 2^(2*n+1)*n^(2*n)/(sqrt(cosh(r)*sin(r)*r)*exp(2*n)*r^(2*n)), where r = 0.93755203435598... is the root of the equation cos(r)*cosh(r) = sin(r)*sinh(r). - Vaclav Kotesovec, Jun 27 2013

EXAMPLE

E.g.f.: A(x) = 1 + x^2/2! + 11*x^4/4! + 311*x^6/6! + 17401*x^8/8! + ...

MAPLE

a:= n-> (2*n)! *coeff(series(1/sqrt(cos(x)*cosh(x)

-sin(x)*sinh(x)), x, 2*n+1), x, 2*n):

seq(a(n), n=0..20); # Alois P. Heinz, Jun 27 2013

MATHEMATICA

Table[n!*SeriesCoefficient[1/Sqrt[Cos[x]*Cosh[x]-Sin[x]*Sinh[x]], {x, 0, n}] , {n, 0, 40, 2}] (* Vaclav Kotesovec, Jun 27 2013 *)

PROG

(PARI) {a(n)=local(X=x+x*O(x^(2*n))); (2*n)!*polcoeff(1/sqrt(cos(X)*cosh(X) - sin(X)*sinh(X)), 2*n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS