The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A347427 Denominators of coefficients in expansion of e.g.f. x / (1 + 2*x - exp(x)). 1

%I #8 Sep 01 2021 22:21:54

%S 1,2,6,1,30,3,42,1,90,5,22,1,2730,35,90,3,1530,45,3990,35,6930,33,

%T 2070,45,40950,91,378,7,870,15,4774,77,13090,595,210,3,383838,1729,

%U 126,21,284130,693,297990,55,217350,2415,29610,315,4873050,16575,131274,1287,157410,1485

%N Denominators of coefficients in expansion of e.g.f. x / (1 + 2*x - exp(x)).

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>

%F a(n) is the denominator of b(n) where b(n) = (1/(n + 1)) * Sum_{k=1..n} binomial(n+1,k+1) * b(n-k), b(0) = 1.

%F a(n) is the denominator of b(n) where b(n) = Bernoulli(n) - 2 * Sum_{k=0..n-1} binomial(n,k) * b(k) * Bernoulli(n-k).

%e 1, 1/2, 5/6, 2, 191/30, 76/3, 5081/42, 674, 386237/90, 153704/5, 5382687/22, 2142054, 55851596621/2730, 7408761716/35, ...

%t nmax = 53; CoefficientList[Series[x/(1 + 2 x - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]! // Denominator

%t b[0] = 1; b[n_] := b[n] = (1/(n + 1)) Sum[Binomial[n + 1, k + 1] b[n - k], {k, 1, n}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 53}]

%t b[0] = 1; b[n_] := b[n] = BernoulliB[n] - 2 Sum[Binomial[n, k] b[k] BernoulliB[n - k], {k, 0, n - 1}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 53}]

%o (PARI) my(x='x+O('x^60)); apply(denominator, Vec(serlaplace(x/(1+2*x-exp(x))))) \\ _Michel Marcus_, Sep 01 2021

%Y Cf. A027641, A027642, A347426 (numerators).

%K nonn,frac

%O 0,2

%A _Ilya Gutkovskiy_, Sep 01 2021

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)