cp's OEIS Frontend

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

%I A308402 #18 Jun 04 2020 02:54:40
%S A308402 1,3,30,105,210,231,30030,2145,72930,969969,9699690,10140585,20281170,
%T A308402 22287,6463230,7713865005,15427730010,90751353,436514007930,
%U A308402 1641030105,134564468610,368217318651,3682173186510,3762220429695,127915494609630,1546231253523,819502564367190,54496920530418135
%N A308402 Denominators of the sequence of rational numbers Rn+ related to Bernoulli numbers.
%C A308402 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).
%C A308402 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.
%H A308402 Frédéric Chapoton, <a href="https://arxiv.org/abs/1905.09012">Ramanujan-Bernoulli numbers as moments of Racah polynomials</a>, arXiv:1905.09012 [math.NT], 2019.
%H A308402 Ludwig Seidel, <a href="http://publikationen.badw.de/de/003384831">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187.
%H A308402 M. B. Villarino, <a href="http://arxiv.org/abs/0707.3950">Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number</a>, arXiv:0707.3950v2 [math.CA], 28 Jul 2007.
%H A308402 M. B. Villarino, <a href="https://www.emis.de/journals/JIPAM/article1026.html">Ramanujan’s Harmonic Number Expansion into Negative Powers of a Triangular Number</a>, Journal of Inequalities in Pure and Applied Mathematics, Volume 9, Issue 3, Article 89.
%e A308402 The sequence Rn+ begins 1, 1/3, 1/30, -1/105, 1/210, -1/231, 191/30030, -29/2145, 2833/72930, ...
%o A308402 (PARI) a(n) = my(p=binomial(x+2, 2)^n); denominator(sum(k=0, poldegree(p), bernfrac(k)*polcoef(p, k, x)));
%Y A308402 Cf. A238813 (numerators of Rn+, for n >0, up to sign).
%K A308402 nonn,frac
%O A308402 0,2
%A A308402 _Michel Marcus_, May 25 2019