A347427 Denominators of coefficients in expansion of e.g.f. x / (1 + 2*x - exp(x)).

1, 2, 6, 1, 30, 3, 42, 1, 90, 5, 22, 1, 2730, 35, 90, 3, 1530, 45, 3990, 35, 6930, 33, 2070, 45, 40950, 91, 378, 7, 870, 15, 4774, 77, 13090, 595, 210, 3, 383838, 1729, 126, 21, 284130, 693, 297990, 55, 217350, 2415, 29610, 315, 4873050, 16575, 131274, 1287, 157410, 1485

Offset

0,2

Links

Table of n, a(n) for n=0..53.

Index entries for sequences related to Bernoulli numbers

Formula

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.

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).

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A027641, A027642, A347426 (numerators).

Sequence in context: A366571 A027642 A249306 * A117214 A185972 A182918

Adjacent sequences: A347424 A347425 A347426 * A347428 A347429 A347430

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Sep 01 2021

Status

approved