OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..360
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)
def A367979_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( exp(-x)/(2-exp(3*x)) ).egf_to_ogf().list()
A367979_list(40) # G. C. Greubel, Jun 11 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2023
STATUS
approved