A002444 Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|. (Formerly M4191 N1747)

1, 6, 30, 84, 90, 132, 5460, 360, 1530, 7980, 13860, 8280, 81900, 1512, 3480, 114576, 117810, 1260, 3838380, 32760, 568260, 1191960, 869400, 236880, 9746100, 525096, 629640, 351120, 198360, 42480, 1362881520, 4324320, 1093950, 33008220, 434700, 843480, 46233287100, 102702600, 1081080

Offset

0,2

Comments

A002443/A002444 = |B_{2n}| (see also A000367/A002445).

References

H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 208.

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).

Links

Table of n, a(n) for n=0..38.

H. T. Davis, Tables of the Mathematical Functions, Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX. [Annotated scan of pages 204-208 of Volume 2.]

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for sequences related to Bernoulli numbers.

Formula

Let p_i denote the i-th prime, and let V(n,i) = floor(n/(prime(i)-1)) = A266742(n,i).

Then a(n) = (Prod_i (p_i)^V(n,i))/n!.

(See Davis, Vol. 2, p. 206, first displayed equation, where a(n) appears as d_{2k}.)

Maple

with(numtheory);
g:=proc(m) local i, n; n:=2*m;
mul(ithprime(i)^floor(n/(ithprime(i)-1)), i=1..pi(n+1));
%/n!;
end;
[seq(g(m), m=0..40)]; # N. J. A. Sloane, Jan 08 2016

Mathematica

a[n_] := Product[Prime[i]^Floor[2n/(Prime[i]-1)], {i, 1, PrimePi[2n+1]}]/(2n)!;
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 08 2023 *)

Crossrefs

Cf. A002443, A000367, A002445, A266742, A266743, A266911.

Sequence in context: A258903 A050972 A259918 * A152788 A055112 A094143

Adjacent sequences: A002441 A002442 A002443 * A002445 A002446 A002447

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

Name amended upon suggestion by T. D. Noe, by M. F. Hasler, Jan 05 2016

Edited with new definition, more terms, and scan of source by N. J. A. Sloane, Jan 08 2016

Status

approved