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A239792
Numerator of b_{2n}(1/4), where b_{n}(x) are Nörlund's generalized Bernoulli polynomials.
3
1, -1, 3, -61, 1261, -4977, 999645, -16820653, 288427601, -1975649524361, 250373334235999, -741069328361243, 2017175162278526957, -16484758150014378103, 1866091048556360006871, -747145289541069391049541, 558035966935526487401599645, -94004035636878314426017611
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
b := proc(n) option remember; if n < 1 then 1 else
-add(binomial(n-1, k-1)*bernoulli(k)*b(n-k)/k, k= 2..n)/2 fi end:
A239792 := n -> numer(b(2*n));
seq(A239792(n), n=0..17);
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
Cf. A220412, A239793 (denominators).
Sequence in context: A279381 A186205 A224451 * A009476 A292110 A173366
KEYWORD
sign,frac
AUTHOR
Peter Luschny, Mar 26 2014
STATUS
approved