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A002444
Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.
(Formerly M4191 N1747)
5
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
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.]
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
KEYWORD
nonn,frac
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