OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
L. Carlitz, The Coefficients of sinh x/sin x, Mathematics Magazine, Vol. 29, No. 4 (Mar. - Apr., 1956), pp. 193-197.
J. M. Gandhi, The coefficients of cosh x/cos x and a note on Carlitz's coefficients of sinh x/sin x, Math. Mag., 31 (1958), 185-191.
FORMULA
Numerator of ( (2n)! times coefficient of x^(2n) in sinh x / sin x ). - corrected by Sean A. Irvine, Apr 17 2019
EXAMPLE
sinh(x)/sin(x) = 1 + 1/3*x^2 + 1/18*x^4 + 13/1890*x^6 + 17/22680*x^8 + ...
MAPLE
a:= n-> numer((2*n)!*coeff(series(sinh(x)/sin(x), x, 2*n+2), x, 2*n)):
seq(a(n), n=0..20); # Alois P. Heinz, Feb 01 2022
MATHEMATICA
nn = 42; t = Range[0, nn]! CoefficientList[Series[Sinh[x]/Sin[x], {x, 0, nn}], x]; t = Numerator[t]; Take[t, {1, nn, 2}] (* T. D. Noe, Jun 21 2012 *)
PROG
(PARI) my(x='x+O('x^40)); select(x->(x!=0), apply(x->numerator(x), Vec(serlaplace(sinh(x)/sin(x))))) \\ Michel Marcus, Apr 16 2019
(Magma)
m:=80; R<x>:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Sinh(x)/Sin(x) )));
[Numerator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // G. C. Greubel, Jan 31 2022
(Sage) [numerator( factorial(2*n)*( sinh(x)/sin(x) ).series(x, 2*n+3).list()[2*n] ) for n in (0..60)] # G. C. Greubel, Jan 31 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved