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A123333 a(n) = 3^n*(Gamma(n+1/3)/Gamma(1/3) + (n-1)!). 1

%I

%S 4,13,82,766,9472,145720,2681200,57411760,1402226560,38468725120,

%T 1171102777600,39174663404800,1428249121868800,56366281606835200,

%U 2393966461645158400,108871544042829568000

%N a(n) = 3^n*(Gamma(n+1/3)/Gamma(1/3) + (n-1)!).

%C The EXP-transform of a(n) is equal to A121630(n).

%H G. C. Greubel, <a href="/A123333/b123333.txt">Table of n, a(n) for n = 1..380</a>

%F E.g.f.: (1-3*x)^(-1/3) - 1 - log(1-3*x).

%t With[{nmax = 50}, CoefficientList[Series[(1 - 3*x)^(-1/3) - 1 - Log[1 - 3*x], {x, 0, nmax}], x] Range[0, nmax]!] (* _G. C. Greubel_, Oct 12 2017 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace((1-3*x)^(-1/3) - 1 - log(1-3*x))) \\ _G. C. Greubel_, Oct 12 2017

%Y Cf. A121630.

%K nonn

%O 1,1

%A _Karol A. Penson_, Sep 26 2006

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)