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A002443 Numerator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.
(Formerly M0906 N0341)
6

%I M0906 N0341 #37 Jan 08 2016 21:01:05

%S 1,1,1,2,3,10,1382,420,10851,438670,7333662,51270780,7090922730,

%T 2155381956,94997844116,68926730208040,1780853160521127,

%U 541314450257070,52630543106106954746,15997766769574912140,10965474176850863126142,1003264444985926729776060,35069919669919290536128980

%N Numerator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.

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

%C a(n) is a nontrivial multiple of A000367(n) if gcd(a(n),A002444(n)) > 1. Furthermore, all terms here are positive, whereas the terms of A000367 retain the sign of B_{2n}, e.g., a(8)/A002444(8) = 10851/1530 is the absolute value of A000367(8)/A002445(8) = -3617/510 = B_{16}. - _M. F. Hasler_, Jan 05 2016

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H H. T. Davis, <a href="/A002443/a002443.pdf">Tables of the Mathematical Functions</a>, 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.]

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%F See Davis, Vol. 2, p. 206, second displayed equation, where a(n) appears as c_{2k}. Note that the recurrence for c_{2k} involves an extra term c_1 = 1 (which is not a term of the present sequence), and also the numbers M_i^{2k} given in A266743. However, given that contemporary Computer Algebra Systems can easily calculate Bernoulli numbers, and A002444 has a simple formula, the best way to compute a(n) today is via a(n) = A002444(n)*|B_{2n}|. - _N. J. A. Sloane_, Jan 08 2016

%Y Cf. A002444, A000367, A002445, A266742, A266743, A266911.

%K nonn,frac

%O 0,4

%A _N. J. A. Sloane_

%E Name amended following a suggestion from _T. D. Noe_. - _M. F. Hasler_, Jan 05 2016

%E Edited with new definition, further terms, and scan of source by _N. J. A. Sloane_, Jan 08 2016

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)