A308402 Denominators of the sequence of rational numbers Rn+ related to Bernoulli numbers.

1, 3, 30, 105, 210, 231, 30030, 2145, 72930, 969969, 9699690, 10140585, 20281170, 22287, 6463230, 7713865005, 15427730010, 90751353, 436514007930, 1641030105, 134564468610, 368217318651, 3682173186510, 3762220429695, 127915494609630, 1546231253523, 819502564367190, 54496920530418135

Offset

0,2

Comments

The sequence Rn+ is defined by Rn+ = psi(binomial(x+2, 2)^n) where the linear form psi is defined by psi(x^n) = Bernoulli(n).

The companion sequence Rn- is defined by Rn+ = psi(binomial(x+1, 2)^n), and differs at n=1 with value -1/6 instead of 1/3.

Links

Table of n, a(n) for n=0..27.

Frédéric Chapoton, Ramanujan-Bernoulli numbers as moments of Racah polynomials, arXiv:1905.09012 [math.NT], 2019.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187.

M. B. Villarino, Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number, arXiv:0707.3950v2 [math.CA], 28 Jul 2007.

M. B. Villarino, Ramanujan’s Harmonic Number Expansion into Negative Powers of a Triangular Number, Journal of Inequalities in Pure and Applied Mathematics, Volume 9, Issue 3, Article 89.

Example

The sequence Rn+ begins 1, 1/3, 1/30, -1/105, 1/210, -1/231, 191/30030, -29/2145, 2833/72930, ...

Prog

(PARI) a(n) = my(p=binomial(x+2, 2)^n); denominator(sum(k=0, poldegree(p), bernfrac(k)*polcoef(p, k, x)));

Crossrefs

Cf. A238813 (numerators of Rn+, for n >0, up to sign).

Sequence in context: A195029 A211617 A180816 * A035328 A100259 A031205

Adjacent sequences: A308399 A308400 A308401 * A308403 A308404 A308405

Keyword

nonn,frac

Author

Michel Marcus, May 25 2019

Status

approved