|
|
A367979
|
|
Expansion of e.g.f. exp(-x) / (2 - exp(3*x)).
|
|
6
|
|
|
1, 2, 22, 278, 4822, 104342, 2709622, 82092278, 2842418902, 110720079062, 4792059271222, 228144844817078, 11849163703935382, 666694458859845782, 40397145162583154422, 2622634244645856386678, 181615748103175019442262, 13362823095925278064444502, 1041037845089466806646007222
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k>=0} (3*k-1)^n / 2^(k+1).
a(n) = (-1)^n + Sum_{k=1..n} binomial(n,k) * 3^k * a(n-k).
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * A000670(k).
|
|
MATHEMATICA
|
nmax = 18; CoefficientList[Series[Exp[-x]/(2 - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = (-1)^n + Sum[Binomial[n, k] 3^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
|
|
PROG
|
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!(Laplace( Exp(-x)/(2-Exp(3*x)) ))); // G. C. Greubel, Jun 11 2024
(SageMath)
P.<x> = PowerSeriesRing(QQ, prec)
return P( exp(-x)/(2-exp(3*x)) ).egf_to_ogf().list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,changed
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|