OFFSET
0,2
COMMENTS
See A286725 for the generalized Lah numbers Lah[2,1].
FORMULA
E.g.f.: d^2/dx^2 (x^2/(2*(1-2*x)^3)) = (1 + 8*x + 4*x^2)/(1 - 2*x)^5.
a(n) = 2^(n-1)*(n+2)!*binomial(n+2,2), n >= 0.
From Amiram Eldar, Dec 11 2022: (Start)
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).
Sum_{n>=0} (-1)^n/a(n) = 24*gamma - 16/sqrt(e) - 24*Ei(-1/2) - 24*log(2). (End)
MATHEMATICA
a[n_] := 2^(n - 1)*(n + 2)! * Binomial[n + 2, 2]; Array[a, 20, 0] (* Amiram Eldar, Dec 11 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 17 2017
STATUS
approved