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%I #14 Jun 28 2019 07:14:48
%S 1,-1,3,-61,1261,-4977,999645,-16820653,288427601,-1975649524361,
%T 250373334235999,-741069328361243,2017175162278526957,
%U -16484758150014378103,1866091048556360006871,-747145289541069391049541,558035966935526487401599645,-94004035636878314426017611
%N Numerator of b_{2n}(1/4), where b_{n}(x) are Nörlund's generalized Bernoulli polynomials.
%D Y. L. Luke, The Special Functions and their Approximations, Vol. 1. Academic Press, 1969, page 34.
%D N. E. Nörlund, Vorlesungen über Differenzenrechnung, Berlin, 1924.
%H J. L. Fields, <a href="http://dx.doi.org/10.1017/S0013091500013171">A note on the asymptotic expansion of a ratio of gamma functions</a>, Proc. Edinburgh Math. Soc. 15 (1) (1966), 43-45.
%F 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)).
%p b := proc(n) option remember; if n < 1 then 1 else
%p -add(binomial(n-1, k-1)*bernoulli(k)*b(n-k)/k, k= 2..n)/2 fi end:
%p A239792 := n -> numer(b(2*n));
%p seq(A239792(n), n=0..17);
%t b[n_] := b[n] = If[n < 1, 1, -Sum[Binomial[n - 1, k - 1] BernoulliB[k] b[n - k]/k, {k, 2, n}]/2];
%t a[n_] := b[2n] // Numerator;
%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Jun 28 2019, from Maple *)
%Y Cf. A220412, A239793 (denominators).
%K sign,frac
%O 0,3
%A _Peter Luschny_, Mar 26 2014
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