A184972 Expansion of e.g.f. 1/( cos(arctanh(x)) - sin(arctanh(x)) ).

1, 1, 3, 13, 81, 605, 5595, 59225, 725985, 9928505, 151720275, 2541096325, 46541735025, 922017392725, 19691502952875, 450278539452625, 10987846186994625, 284800630720672625, 7817729823142243875, 226487095510937568125, 6907505385375525620625

Offset

0,3

Comments

Compare e.g.f. to 1/(cosh(arctanh(x)) - sinh(arctanh(x))) = sqrt((1+x)/(1-x)).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) ~ n!*2*sqrt(2)*exp(Pi/2)/(exp(Pi)-1) * ((exp(Pi/2)+1)/(exp(Pi/2)-1))^n. - Vaclav Kotesovec, Oct 18 2013

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 81*x^4/4! + 605*x^5/5! + ...
where 1/A(tanh(x)) = cos(x) + sin(x).

Mathematica

CoefficientList[Series[1/(Sqrt[2]*Sin[Pi/4 + 1/2*Log[(1-x)/(1+x)]]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 18 2013 *)

Prog

(PARI) {a(n)=n!*polcoeff(1/(cos(atanh(x+x*O(x^n)))-sin(atanh(x+x*O(x^n)))), n)}

Crossrefs

Sequence in context: A331643 A074514 A020014 * A160882 A135921 A005923

Adjacent sequences: A184969 A184970 A184971 * A184973 A184974 A184975

Keyword

nonn

Author

Paul D. Hanna, Dec 22 2011

Status

approved