A002443 Numerator in Feinler's formula for unsigned Bernoulli number |B_{2n}|.

1, 1, 1, 2, 3, 10, 1382, 420, 10851, 438670, 7333662, 51270780, 7090922730, 2155381956, 94997844116, 68926730208040, 1780853160521127, 541314450257070, 52630543106106954746, 15997766769574912140, 10965474176850863126142, 1003264444985926729776060, 35069919669919290536128980

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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.]
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

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

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

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