

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
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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

Table of n, a(n) for n=0..22.
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 204208 of Volume 2.]
Index entries for sequences related to Bernoulli numbers.


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

Cf. A002444, A000367, A002445, A266742, A266743, A266911.
Sequence in context: A218271 A128125 A070239 * A111788 A238455 A098929
Adjacent sequences: A002440 A002441 A002442 * A002444 A002445 A002446


KEYWORD

nonn,frac


AUTHOR

N. J. A. Sloane


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



