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A002443 Numerator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.
(Formerly M0906 N0341)
6
1, 1, 1, 2, 3, 10, 1382, 420, 10851, 438670, 7333662, 51270780, 7090922730, 2155381956, 94997844116, 68926730208040, 1780853160521127, 541314450257070, 52630543106106954746, 15997766769574912140, 10965474176850863126142, 1003264444985926729776060, 35069919669919290536128980 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A002443/A002444 = |B_{2n}| (see also A000367/A002445).
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
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
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
CROSSREFS
Sequence in context: A128125 A351775 A070239 * A111788 A238455 A098929
KEYWORD
nonn,frac
AUTHOR
EXTENSIONS
Name amended following a suggestion from T. D. Noe. - M. F. Hasler, Jan 05 2016
Edited with new definition, further terms, and scan of source by N. J. A. Sloane, Jan 08 2016
STATUS
approved

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Last modified June 18 15:05 EDT 2024. Contains 373481 sequences. (Running on oeis4.)