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A337026
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a(n) = (2/3) * Sum_{k>=0} (2*k + 1)^n / 3^k.
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3
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1, 2, 7, 38, 277, 2522, 27547, 351038, 5112457, 83764082, 1524907087, 30536665238, 667096092637, 15787642820042, 402374890155427, 10987722264846638, 320046586135452817, 9904844539648850402, 324568009210656076567, 11226512280285374623238
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OFFSET
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0,2
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LINKS
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FORMULA
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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) = 1 + Sum_{k=1..n} 2^(k-1) * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 24 2023
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MATHEMATICA
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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]!
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 2*Exp(x)/(3-Exp(2*x)) ))); // G. C. Greubel, Jun 09 2022
(Sage)
P.<x> = PowerSeriesRing(QQ, prec)
return P( 2*exp(x)/(3-exp(2*x)) ).egf_to_ogf().list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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