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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..17.

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

Adjacent sequences:  A239789 A239790 A239791 * A239793 A239794 A239795

KEYWORD

sign,frac

AUTHOR

Peter Luschny, Mar 26 2014

STATUS

approved

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Last modified August 4 15:44 EDT 2021. Contains 346447 sequences. (Running on oeis4.)