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A184972 Expansion of e.g.f. 1/( cos(arctanh(x)) - sin(arctanh(x)) ). 0
1, 1, 3, 13, 81, 605, 5595, 59225, 725985, 9928505, 151720275, 2541096325, 46541735025, 922017392725, 19691502952875, 450278539452625, 10987846186994625, 284800630720672625, 7817729823142243875, 226487095510937568125, 6907505385375525620625 (list; graph; refs; listen; history; text; internal format)
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).

MAPLE

a:=series(1/(cos(arctanh(x))-sin(arctanh(x))), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 28 2019

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

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Last modified December 4 22:42 EST 2021. Contains 349526 sequences. (Running on oeis4.)