A001905 From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1). (Formerly M5051 N2184)

1, 17, 1835, 195013, 3887409, 58621671097, 327585142651, 83717985168643, 189605076148138997, 595202561342135705333, 26162958970171926774263, 822117399240965474306397043, 4746533358587697361080419575

Offset

1,2

References

N. E. Nørlund, Vorlesungen über Differenzenrechnung. Springer-Verlag, Berlin, 1924, p. 463.

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

Gheorghe Coserea, Table of n, a(n) for n = 1..200

Guodong Liu, A Recurrence Formula for D Numbers D2n(2n-1), Discrete Dynamics in Nature and Society, Volume 2009 (2009). [From Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 26 2010]

N. E. Nørlund, Vorlesungen über Differenzenrechnung Springer 1924, p. 463. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 26 2010]

Index entries for sequences related to Bernoulli numbers.

Mathematica

NorlundD[nu_, n_] := (-2)^nu NorlundB[nu, n, n/2];
Table[NorlundD[2n, 2n-1] // Numerator // Abs, {n, 1, 13}] (* Jean-François Alcover, Jul 02 2019 *)

Prog

(PARI) x='x+O('x^33); abs(apply(numerator, select(i->i, Vec(-1 + serlaplace((x / log(x + sqrt(1+x^2)))^2 / sqrt(1+x^2)))))) \\ Gheorghe Coserea, Aug 10 2015

Crossrefs

Cf. A001904, A261272 (denominator), A261274.

Sequence in context: A156675 A276808 A088465 * A221322 A135505 A171704

Adjacent sequences: A001902 A001903 A001904 * A001906 A001907 A001908

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 26 2010

Status

approved