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%I #18 Dec 11 2022 06:03:33
%S 1,18,288,4800,86400,1693440,36126720,836075520,20901888000,
%T 562028544000,16186422067200,497364605337600,16247243774361600,
%U 562404592189440000,20567939371499520000,792551263781781504000,32098326183162150912000,1363234794367239585792000
%N Third column of triangle A286724: Lah[2,1](n+2, 2), n >= 0.
%C See A286725 for the generalized Lah numbers Lah[2,1].
%F E.g.f.: d^2/dx^2 (x^2/(2*(1-2*x)^3)) = (1 + 8*x + 4*x^2)/(1 - 2*x)^5.
%F a(n) = 2^(n-1)*(n+2)!*binomial(n+2,2), n >= 0.
%F From _Amiram Eldar_, Dec 11 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 32 - 16*sqrt(e) + 8*gamma - 8*Ei(1/2) - 8*log(2), where Ei(x) is the exponential integral and gamma is Euler's constant (A001620).
%F Sum_{n>=0} (-1)^n/a(n) = 24*gamma - 16/sqrt(e) - 24*Ei(-1/2) - 24*log(2). (End)
%t a[n_] := 2^(n - 1)*(n + 2)! * Binomial[n + 2, 2]; Array[a, 20, 0] (* _Amiram Eldar_, Dec 11 2022 *)
%Y Cf. A000165 (m=0), A014479 (m=1), A001620, A051578, A051580, A051582, A286724.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 17 2017
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