|
|
A346208
|
|
Expansion of e.g.f.: exp(-3*x) / (2 - exp(x)).
|
|
5
|
|
|
1, -2, 6, -14, 54, -62, 966, 4786, 71574, 875938, 12810726, 202739986, 3511712694, 65856494338, 1330170266886, 28785391689586, 664456856787414, 16296345814039138, 423191833100881446, 11600198414334789586, 334710974532291679734, 10140603124807778534338
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} binomial(n,k) * (-3)^(n-k) * A000670(k).
a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * k! * A002620(k+2).
a(n) = Sum_{k>=0} (k - 3)^n / 2^(k+1).
a(n) = (-3)^n + Sum_{k=0..n-1} binomial(n,k) * a(k).
|
|
MATHEMATICA
|
nmax = 21; CoefficientList[Series[Exp[-3 x]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[HurwitzLerchPhi[1/2, -n, -3]/2, {n, 0, 21}]
a[n_] := a[n] = (-3)^n + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]
|
|
PROG
|
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!(Laplace( Exp(-3*x)/(2-Exp(x)) ))); // G. C. Greubel, Jun 11 2024
(SageMath)
P.<x> = PowerSeriesRing(QQ, prec)
return P( exp(-3*x)/(2-exp(x)) ).egf_to_ogf().list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|