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 A344037 Expansion of e.g.f.: exp(-2*x) / (2 - exp(x)). 8
 1, -1, 3, -1, 27, 119, 1203, 11759, 136587, 1771559, 25562403, 405657119, 7022893947, 131714582999, 2660335750803, 57570797728079, 1328913670528107, 32592691757218439, 846383665814342403, 23200396829831840639, 669421949061096575067, 20281206249626017421879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..420 FORMULA a(n) = Sum_{k=0..n} binomial(n,k) * (-2)^(n-k) * A000670(k). a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * k! * A008619(k). a(n) = Sum_{k>=0} (k - 2)^n / 2^(k+1). a(n) = (-2)^n + Sum_{k=0..n-1} binomial(n,k) * a(k). a(n) ~ n! / (8 * log(2)^(n+1)). - Vaclav Kotesovec, Aug 15 2021 MATHEMATICA nmax = 21; CoefficientList[Series[Exp[-2 x]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]! Table[HurwitzLerchPhi[1/2, -n, -2]/2, {n, 0, 21}] a[n_] := a[n] = (-2)^n + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}] PROG (Magma) R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp(-2*x)/(2-Exp(x)) ))); // G. C. Greubel, Jun 11 2024 (SageMath) def A344037_list(prec): P. = PowerSeriesRing(QQ, prec) return P( exp(-2*x)/(2-exp(x)) ).egf_to_ogf().list() A344037_list(40) # G. C. Greubel, Jun 11 2024 CROSSREFS Cf. A000670, A007047, A008619, A052841, A330603, A346208. Sequence in context: A138545 A271806 A270289 * A260902 A165624 A287206 Adjacent sequences: A344034 A344035 A344036 * A344038 A344039 A344040 KEYWORD sign AUTHOR Ilya Gutkovskiy, Aug 01 2021 STATUS approved

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Last modified August 13 22:54 EDT 2024. Contains 375146 sequences. (Running on oeis4.)