A002445 -id:A002445 - cp's OEIS frontend

A120082 Numerators of expansion for Debye function for n=1: D(1,x).

1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 77683, 0, -236364091, 0, 657931, 0, -3392780147, 0, 1723168255201, 0, -7709321041217, 0, 151628697551, 0, -26315271553053477373, 0, 154210205991661, 0, -261082718496449122051

Offset: 0

Wolfdieter Lang, Jul 20 2006

Denominators are found under A120083.
D(1,x) = (1/x)*integral_{t=0..x} t/(exp(t)-1) dt (note the factor x on the r.h.s. of  the Abramowitz-Stegun link). This is the e.g.f. for {Bernoulli(n)/(n+1)}A027641(n)/A227540(n).%20Thanks%20to%20_Peter%20Luschny">{n>=0}. See A027641(n)/A227540(n). Thanks to _Peter Luschny for asking me to revisit this sequence. - Wolfdieter Lang, Jul 15 2013
Also numerators of coefficients in expansion of x/(exp(x)-1). See A227830 for denominators. - N. J. A. Sloane, Aug 01 2013

			Rationals r(n): [1, -1/4, 1/36, 0, -1/3600, 0, 1/211680, 0, -1/10886400, ...].

M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 23.

Peter Luschny, Table of n, a(n) for n = 0..500
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, pp. 998, equ. 27.1.1 for n=1, with a factor x extracted.
Wolfdieter Lang, Rationals r(n).

Cf. A060054, A060055, A120083, A182918, A227540, A227830, A358625.

[Numerator(Bernoulli(n)/Factorial(n+1)): n in [0..50]]; // G. C. Greubel, May 01 2023

A120082 := proc(n) local b; if n = 0 then b := 1 ; elif n = 1 then b := -1/4 ; elif type(n, 'odd') then b := 0; else b := bernoulli(n)/(n+1)! ; fi; numer(b) ; end: # R. J. Mathar, Sep 03 2009
gf := (1 - x/4 + sum((bernoulli(2*k)/((2*k+1)*(2*k)!))*x^(2*k), k=0..infinity)):
a := proc(n) local ser; if n = 0 then return 1 fi; ser := series(gf, x, n+2):
numer(coeff(ser, x, n)) end: seq(a(n), n = 0..40); # Peter Luschny, Dec 02 2022

Table[Numerator[BernoulliB[n]/((n+1)!)], {n,0,50}] (* G. C. Greubel, May 01 2023 *)

def A120082(n): return numerator(bernoulli(n)/factorial(n+1))
[A120082(n) for n in range(51)] # G. C. Greubel, May 01 2023

a(n) = numerator(r(n)), with r(n) = [x^n] (1 - x/4 + Sum_{k>=0} (B(2*k)/((2*k+1)*(2*k)!))*x^(2*k)), |x| < 2*Pi. B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).
a(n) = numerator(B(n)/(n+1)!), n >= 0. See the above comment on the e.g.f. D(1,x). - Wolfdieter Lang, Jul 15 2013
Apart from the sign of a(1) this sequence differs from A358625 for the first time at n = 68. - Peter Luschny, Dec 02 2022

Edited after Andrey Zabolotskiy noticed an inconsistency by Peter Luschny, Dec 02 2022

A282773 Numbers n such that Bernoulli number B_{n} has denominator 498.

Original entry on oeis.org

82, 574, 1066, 1394, 3034, 3362, 3854, 4838, 5494, 5822, 6478, 7462, 7954, 8282, 8774, 8938, 10414, 11234, 12218, 12382, 12874, 13694, 15826, 16154, 17302, 18614, 18778, 21074, 21238, 21566, 22058, 22222, 22714, 23206, 23534, 23698, 25174, 25502, 25994

Offset: 1

Paolo P. Lava, Mar 07 2017

nonn

498 = 2 * 3 * 83.
All terms are multiples of a(1) = 82.
For these numbers numerator(B_{n}) mod denominator(B_{n}) = 77.
n such that 82 | n but there are no primes p other than 2, 3, 83 such that p-1 | n. - Robert Israel, Mar 07 2017

			Bernoulli B_{82} is 1677014149185145836823154509786269900207736027570253414881613/498, hence 82 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Von Staudt-Clausen theorem

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Cf. A002445.

with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,498);
# Alternative:
filter:= n ->
  select(isprime,map(`+`,numtheory:-divisors(n),1)) = {2,3,83}:
select(filter, [seq(i,i=82..10^5,82)]); # Robert Israel, Mar 07 2017

Select[82 Range[360], Denominator@ BernoulliB@ # == 498 &] (* Michael De Vlieger, Mar 07 2017 *)

More terms from Michael De Vlieger, Mar 07 2017

A060054 Numerators of numbers appearing in the Euler-Maclaurin summation formula.

Original entry on oeis.org

-1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 77683, 0, -236364091, 0, 657931, 0, -3392780147, 0, 1723168255201, 0, -7709321041217, 0, 151628697551, 0, -26315271553053477373

Offset: 1

Wolfdieter Lang, Feb 16 2001

a(n+1) = numerator(-Zeta(-n)), n>=1, with Riemann's zeta function. a(1)=-1=-numerator(-Zeta(-0)). For denominators see A075180.
Comment from N. J. A. Sloane, Oct 15 2008: (Start)
It appears that essentially the same sequence of rational numbers arises when we expand 1/(exp(1/x)-1) for large x. Here is the result of applying Bruno Salvy's gdev Maple program (answering a question raised by Roger L. Bagula):
gdev(1/(exp(1/x)-1), x=infinity, 20);
x - 1/2 + (1/12)/x - (1/720)/x^3 + (1/30240)/x^5 - (1/1209600)/x^7 + (1/47900160)/x^9 - (691/1307674368000)/x^11 + (1/74724249600)/x^13 - (3617/10670622842880000)/x^15 + (43867/5109094217170944000)/x^17 - (174611/802857662698291200000)/x^19 + ... (End)

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).

Vincenzo Librandi, Table of n, a(n) for n = 1..600
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 16 (3.6.28), p. 806 (23.1.30), p. 886 (25.4.7).
Zhanna Kuznetsova and Francesco Toppan, Classification of minimal Z_2 X Z_2-graded Lie (super)algebras and some applications, arXiv:2103.04385 [math-ph], 2021.

Denominators of nonzero numbers give A060055.
Cf. A001067 (numerator of B(2*k)/(2*k)).
Cf. A075180.
Cf. also A120082/A227830.
Cf. A242179, A106831, A000142.

a060054 n = a060054_list !! n
a060054_list = -1 : map (numerator . sum) (tail $ zipWith (zipWith (%))
   (zipWith (map . (*)) a000142_list a242179_tabf) a106831_tabf)
-- Reinhard Zumkeller, Jul 04 2014

a[m_] := Sum[(-2)^(-k-1) k! StirlingS2[m,k],{k,0,m}]/(2^(m+1)-1); Table[Numerator[a[i]], {i,0,30}] (* Peter Luschny, Apr 29 2009 *)

a(n):=num((-1)^n*sum(binomial(n+k-1,n-1)*sum((j!*(-1)^(j)*binomial(k,j)*stirling1(n+j,j))/(n+j)!,j,1,k),k,1,n)); /* Vladimir Kruchinin, Feb 03 2013 */

a(n) = numerator(b(n)) with b(1) = -1/2; b(2*k+1) = 0, k >= 1; b(2*k) = B(2*k)/(2*k)! (B(2*n) = B_{2n} Bernoulli numbers: numerators A000367, denominators A002445)

A090801 List of distinct numbers appearing as denominators of Bernoulli numbers.

Original entry on oeis.org

1, 2, 6, 30, 42, 66, 138, 282, 330, 354, 498, 510, 642, 690, 798, 870, 1002, 1074, 1362, 1410, 1434, 1518, 1578, 1590, 1770, 1806, 2082, 2154, 2298, 2478, 2490, 2658, 2730, 2802, 2874, 3018, 3102, 3210, 3318, 3378, 3486, 3522, 3882, 3894, 3954, 4110, 4314

Offset: 1

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Feb 10 2004

From Dean Hickerson, Oct 19 2007: (Start)
Except for a(0)=1, all denominators in A002445 are divisible by 6 and are squarefree. To test such a number k to see if it's in the sequence, let 2n be the least common multiple of all p-1 for which p is a prime divisor of k.
Now list the primes p such that p-1 divides 2n. If all of them are divisors of k, then k is in the sequence; otherwise it's not.
For example, consider k = 78 = 2 * 3 * 13. The LCM of 2-1, 3-1 and 13-1 is 12, so 2n=12. The primes p such that p-1 divides 12 are 2, 3, 5, 7 and 13. Since 5 and 7 are not divisors of 78, 78 is not in the sequence. (End)
From Paul Curtz, Oct 19 2012: (Start)
a(n+3) mod 9 = 6,3,6,3,3,3,6,3,3,6,3,6,6,6,.... (Also a(n+3) in base 9 mod 10.)
(a(n+2)-2)/4 = 0, 1, 7, 10, 16, 34, 70, 82, 88, 124, .... See A002445.
(a(n+4) - a(n+3))/12 = 2, 1, 3, 6, 12, 4, 2, 12, 1, 11, .... Is this always an integer? (End)

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

T. D. Noe, Table of n, a(n) for n = 1..1001

Cf. A090810, A002445 (denominators of Bernoulli numbers B_2n).

Take[Union@Table[Denominator[BernoulliB[k]], {k, 0, 2000}], 80] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

is(n)=if(n==1, 1, my(f=factor(n)); if(vecmax(f[,2])>1, return(0));fordiv(lcm(apply(k->k-1, f[,1])), k, if(isprime(k+1) && n%(k+1), return(0)));1) \\ Charles R Greathouse IV, Nov 26 2012

We know from the von Staudt-Clausen theorem (see Rademacher) that the denominator of the Bernoulli number B_{2k} is the product of those distinct primes p for which p-1 divides 2k. In particular, all numbers after the first two (which are the denominators of B_0 and B_1) are divisible by 6. - N. J. A. Sloane, Feb 10 2004

Extended by Robert G. Wilson v, Feb 10 2004

A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

Original entry on oeis.org

1, 1, -1, 1, -3, 5, -691, 35, -3617, 43867, -1222277, 854513, -1181820455, 76977927, -23749461029, 8615841276005, -84802531453387, 90219075042845, -26315271553053477373, 38089920879940267, -261082718496449122051, 1520097643918070802691

Offset: 0

N. J. A. Sloane

			(n+1)*B_n gives: 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Seiichi Manyama, Table of n, a(n) for n = 0..314 (terms 0..100 from T. D. Noe)
L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.
M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.
Index entries for sequences related to Bernoulli numbers.

Denominators are in A006955.

Cf. A050925/A050932, A000367/A002445.

[Numerator((2*n+1)*Bernoulli(2*n)): n in [1..30]]; // G. C. Greubel, Jul 03 2019

gf := z / (1 - exp(-z)): ser := series(gf, z, 84):
seq(numer((n+1)!*coeff(ser, z, n)), n=0..42, 2); # Peter Luschny, Aug 29 2020

Table[Numerator[2(2n+1)BernoulliB[2n]], {n, 1, 30}]

a(n) = numerator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017

[numerator((2*n+1)*bernoulli(2*n)) for n in (1..30)] # G. C. Greubel, Jul 03 2019

A006955 Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

Original entry on oeis.org

1, 2, 6, 6, 10, 6, 210, 2, 30, 42, 110, 6, 546, 2, 30, 462, 170, 6, 51870, 2, 330, 42, 46, 6, 6630, 22, 30, 798, 290, 6, 930930, 2, 102, 966, 10, 66, 1919190, 2, 30, 42, 76670, 6, 680862, 2, 690, 38874, 470, 6, 46410, 2, 330, 42, 106, 6, 1919190

Offset: 0

Simon Plouffe and N. J. A. Sloane

Also denominators of asymptotic expansion of polygamma function psi''(z).

			(n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260, (6.4.13).
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260, (6.4.13).
L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.
M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.
Index entries for sequences related to Bernoulli numbers.

Numerators are in A002427.

Cf. A050925/A050932, A000367/A002445, A006956, A123125.

gf := z / (1 - exp(-z)): ser := series(gf, z, 220):
seq(denom((n+1)!*coeff(ser, z, n)), n=0..108, 2); # Peter Luschny, Aug 29 2020

Denominator[Table[(2n+1)BernoulliB[2n],{n,0,60}]] (* Harvey P. Dale, Nov 03 2011 *)

a(n) = denominator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017

Apparently a(n) = denominator(Sum_{k=0..2*n-1} (-1)^(2*n-k+1)*E1(2*n, k+1)/ binomial(2*n, k+1)), where E1(n, k) denotes the first-order Eulerian numbers A123125. - Peter Luschny, Feb 17 2021

A176591 Bernoulli denominators A141056(n), with the exception a(1)=1.

Original entry on oeis.org

1, 1, 6, 2, 30, 2, 42, 2, 30, 2, 66, 2, 2730, 2, 6, 2, 510, 2, 798, 2, 330, 2, 138, 2, 2730, 2, 6, 2, 870, 2, 14322, 2, 510, 2, 6, 2, 1919190, 2, 6, 2, 13530, 2, 1806, 2, 690, 2, 282, 2, 46410, 2, 66, 2, 1590, 2, 798, 2, 870, 2, 354, 2, 56786730, 2, 6, 2, 510, 2, 64722, 2, 30, 2, 4686, 2, 140100870, 2, 6, 2, 30, 2

Offset: 0

Paul Curtz, Apr 21 2010

These are also the denominators of a sequence generated by inverse binomial transform of a modified Bernoulli sequence described in (with numerators in) A176328.

Antti Karttunen, Table of n, a(n) for n = 0..4096

Cf. A141056, A160014.

read("transforms") ; evb := [1, 0, seq(bernoulli(n), n=2..50)] ; BINOMIALi(evb) ; apply(denom, %) ; # R. J. Mathar, Dec 01 2010
seq(denom((bernoulli(i,1)+bernoulli(i,2))/2),i=0..50); # Peter Luschny, Jun 17 2012

a[n_] := If[OddQ[n], 2, BernoulliB[n] // Denominator]; a[1] = 1; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 29 2012 *)
Join[{1,1},BernoulliB[Range[2,80]]/.(0->1/2)//Denominator] (* Harvey P. Dale, Dec 31 2018 *)

A176591(n) = { my(p=1); if(n>1, fordiv(n, d, my(r=d+1); if(isprime(r), p = p*r))); return(p); }; \\ Antti Karttunen, Dec 20 2018, after code in A141056

a(n) = A141056(n), n <> 1.
a(n) = A027760(n), n>1.
a(2n) = A002445(n), a(2n+1)= A040000(n).

More terms from Antti Karttunen, Dec 20 2018

A050925 Numerator of (n+1)*Bernoulli(n).

Original entry on oeis.org

1, -1, 1, 0, -1, 0, 1, 0, -3, 0, 5, 0, -691, 0, 35, 0, -3617, 0, 43867, 0, -1222277, 0, 854513, 0, -1181820455, 0, 76977927, 0, -23749461029, 0, 8615841276005, 0, -84802531453387, 0, 90219075042845, 0, -26315271553053477373, 0, 38089920879940267, 0

Offset: 0

N. J. A. Sloane, Dec 30 1999

The denominators are in A050932. The e.g.f. for (n+1)*Bernoulli(n), n >= 0, is (d/dx)(x^2/(exp(x)-1)) = x*(2*(exp(x)-1)- x*exp(x))/(exp(x)-1)^2. - Wolfdieter Lang, Jul 15 2013
It can be observed that the rational sequence [0, 1, 1, 1/2, 0, -1/6, 0, 1/6, 0, -3/10, 0, 5/6, ...], derived from a(n)/A050932(n), is an autosequence of the first kind. - Jean-François Alcover, Jul 21 2017
Apparently a(n) = numerator(Sum_{k=0..n-1} (-1)^(n-k+1)*E1(n,k+1)/binomial(n,k+1)) for n >= 2, where E1(n, k) denotes the first-order Eulerian numbers A123125. - Peter Luschny, Feb 17 2021

N. J. A. Sloane, Table of n, a(n) for n = 0..200
M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193.
OEIS Wiki, Autosequence
S. C. Woon, A tree for generating Bernoulli numbers, Math. Mag., 70 (1997), 51-56.
Index entries for sequences related to Bernoulli numbers.

Cf. A050932, A000367/A002445, A002882, A003245, A127187, A127188, A242179, A106831, A000142, A123125.

a050925 n = a050925_list !! n
a050925_list = 1 : -1 : (tail $ map (numerator . sum) $
   zipWith (zipWith (%))
   (zipWith (map . (*)) (drop 2 a000142_list) a242179_tabf) a106831_tabf)
-- Reinhard Zumkeller, Jul 04 2014

Numerator[Table[(n+1)BernoulliB[n],{n,0,40}]] (* Harvey P. Dale, May 13 2012 *)

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

A050932 Denominator of (n+1)*Bernoulli(n).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 30 1999

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

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.

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

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

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

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

from sympy import bernoulli, gcd
def A050932(n):
    q = bernoulli(n).q
    return q//gcd(q,n+1) # Chai Wah Wu, Apr 02 2021

A120083 Denominators of expansion for Debye function for n=1: D(1,x).

Original entry on oeis.org

1, 4, 36, 1, 3600, 1, 211680, 1, 10886400, 1, 526901760, 1, 16999766784000, 1, 1120863744000, 1, 181400588328960000, 1, 97072790126247936000, 1, 16860010916664115200000, 1, 324325300906011525120000, 1

Offset: 0

Wolfdieter Lang, Jul 20 2006

Numerators are found under A120082.

G. C. Greubel, Table of n, a(n) for n = 0..447

Cf. A120082.

[Denominator(Bernoulli(n)/Factorial(n+1)): n in [0..50]]; // G. C. Greubel, May 01 2023

Table[Denominator[BernoulliB[n]/(n+1)!], {n,0,50}] (* G. C. Greubel, May 01 2023 *)

def A120083(n): return denominator(bernoulli(n)/factorial(n+1))
[A120083(n) for n in range(51)] # G. C. Greubel, May 01 2023

a(n) = denominator(r(n)), with r(n) = [x^n]( 1 - x/4 + Sum_{k >= 0}(B(2*k)/((2*k+1)*(2*k)!))*x^(2*k) ), |x|<2*pi. B(2*k) = A000367(k)/A002445(k) (Bernoulli numbers).

a(n) = denominator(B(n)/(n+1)!), n >= 0. See the comment on the e.g.f. D(1,x) in A120082. - Wolfdieter Lang, Jul 15 2013

cp's OEIS Frontend

A120082 Numerators of expansion for Debye function for n=1: D(1,x).

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A282773 Numbers n such that Bernoulli number B_{n} has denominator 498.

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A060054 Numerators of numbers appearing in the Euler-Maclaurin summation formula.

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A090801 List of distinct numbers appearing as denominators of Bernoulli numbers.

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A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

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Magma

Maple

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Sage

A006955 Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.

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Maple