OFFSET
0,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..224 (terms 0..100 from T. D. Noe)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.68).
M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 30.
J. Malenfant, Factorization of and Determinant Expressions for the Hypersums of Powers of Integers, arXiv preprint arXiv:1104.4332 [math.NT], 2011.
Eric Weisstein's World of Mathematics, Hyperbolic Cosecant
Eric Weisstein's World of Mathematics, Cosecant
Index entries for Bernoulli numbers B(2n)
FORMULA
A036280(n)/a(n)= 2 *(2^(2n-1) -1) *abs(B(2n)) / (2n)!.
From Arkadiusz Wesolowski, Oct 16 2013: (Start)
a(n) = A036280(n)*Pi^(2*n)/(zeta(2*n)*(2 - (2^(1-n))^2)).
a(n) = A230265(n)/2. (End)
EXAMPLE
cosec(x) = x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+...
1, 1/6, 7/360, 31/15120, 127/604800, 73/3421440, 1414477/653837184000, 8191/37362124800, ...
MAPLE
series(csc(x), x, 60);
MATHEMATICA
a[n_] := 2(2^(2n-1)-1) Abs[BernoulliB[2n]]/(2n)! // Denominator;
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jul 14 2018 *)
PROG
(Sage)
def A036281_list(len):
R, C = [1], [1]+[0]*(len-1)
for n in (1..len-1):
for k in range(n, 0, -1):
C[k] = -C[k-1] / (k*(4*k+2))
C[0] = -sum(C[k] for k in (1..n))
R.append(C[0].denominator())
return R
print(A036281_list(15)) # Peter Luschny, Feb 21 2016
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved