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A050932 Denominator of (n+1)*Bernoulli(n). 10
1, 1, 2, 1, 6, 1, 6, 1, 10, 1, 6, 1, 210, 1, 2, 1, 30, 1, 42, 1, 110, 1, 6, 1, 546, 1, 2, 1, 30, 1, 462, 1, 170, 1, 6, 1, 51870, 1, 2, 1, 330, 1, 42, 1, 46, 1, 6, 1, 6630, 1, 22, 1, 30, 1, 798, 1, 290, 1, 6, 1, 930930, 1, 2, 1, 102, 1, 966, 1, 10, 1, 66, 1, 1919190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Apparently a(n) = denominator(Sum_{k=0..n-1} (-1)^(n-k+1)*E1(n, k+1)/binomial(n, k+1)), where E1(n, k) denotes the first-order Eulerian numbers A123125. - Peter Luschny, Feb 17 2021

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..20000 (terms 0..200 from N. J. A. Sloane)

M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.

S. C. Woon, A tree for generating Bernoulli numbers, Math. Mag., 70 (1997), 51-56.

Index entries for sequences related to Bernoulli numbers.

MATHEMATICA

Denominator/@Table[(n+1)BernoulliB[n], {n, 0, 80}] (* Harvey P. Dale, May 19 2011 *)

PROG

(Haskell)

a050932 n = a050932_list !! n

a050932_list = 1 : map (denominator . sum) (zipWith (zipWith (%))

(zipWith (map . (*)) (drop 2 a000142_list) a242179_tabf) a106831_tabf)

-- Reinhard Zumkeller, Jul 04 2014

(PARI) a(n)=denominator(bernfrac(n)*(n+1)) \\ Charles R Greathouse IV, Feb 07 2017

(Python)

from sympy import bernoulli, gcd

def A050932(n):

q = bernoulli(n).q

return q//gcd(q, n+1) # Chai Wah Wu, Apr 02 2021

CROSSREFS

Cf. A050925, A000367/A002445, A027641/A027642, A002882, A003245, A127187, A127188, A242179, A106831, A000142, A123125.

Sequence in context: A318503 A328580 A088123 * A286515 A166120 A318256

Adjacent sequences: A050929 A050930 A050931 * A050933 A050934 A050935

KEYWORD

nonn,frac,nice,easy

AUTHOR

N. J. A. Sloane, Dec 30 1999

STATUS

approved

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Last modified December 7 08:24 EST 2022. Contains 358649 sequences. (Running on oeis4.)