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A002444
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Denominator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.
(Formerly M4191 N1747)
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5
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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
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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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).
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LINKS
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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.]
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FORMULA
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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}.)
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MAPLE
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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;
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MATHEMATICA
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a[n_] := Product[Prime[i]^Floor[2n/(Prime[i]-1)], {i, 1, PrimePi[2n+1]}]/(2n)!;
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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Edited with new definition, more terms, and scan of source by N. J. A. Sloane, Jan 08 2016
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STATUS
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approved
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