OFFSET
0,3
REFERENCES
Y. L. Luke, The Special Functions and their Approximations, Vol. 1. Academic Press, 1969, page 34.
N. E. Nörlund, Vorlesungen über Differenzenrechnung, Berlin, 1924.
LINKS
J. L. Fields, A note on the asymptotic expansion of a ratio of gamma functions, Proc. Edinburgh Math. Soc. 15 (1) (1966), 43-45.
FORMULA
Let b(n) = -Sum_{k=2..n} (C(n-1, k-1)*Bernoulli(k)*b(n-k)/k)/2 for n>0 and otherwise 1. Then a(n) = numerator(b(2*n)).
MAPLE
MATHEMATICA
b[n_] := b[n] = If[n < 1, 1, -Sum[Binomial[n - 1, k - 1] BernoulliB[k] b[n - k]/k, {k, 2, n}]/2];
a[n_] := b[2n] // Numerator;
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jun 28 2019, from Maple *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Peter Luschny, Mar 26 2014
STATUS
approved