OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
FORMULA
E.g.f.: 2 * exp(x) / (3 - exp(2*x)).
a(n) = Sum_{k=0..n} binomial(n,k) * A122704(k).
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A123227(k).
a(n) ~ n! * 2^(n+1) / (sqrt(3) * log(3)^(n+1)). - Vaclav Kotesovec, Mar 27 2022
a(n) = 1 + Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 24 2023
MATHEMATICA
Table[2^(n + 1) HurwitzLerchPhi[1/3, -n, 1/2]/3, {n, 0, 19}]
nmax = 19; CoefficientList[Series[2 Exp[x]/(3 - Exp[2 x]), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 2*Exp(x)/(3-Exp(2*x)) ))); // G. C. Greubel, Jun 09 2022
(Sage)
def A337026_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 2*exp(x)/(3-exp(2*x)) ).egf_to_ogf().list()
A337026_list(40) # G. C. Greubel, Jun 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2020
STATUS
approved