A002444 Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.
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
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
- 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.
Programs
-
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 *)
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}.)
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
Comments