A327606 - OEIS

%I #15 Mar 15 2020 17:39:55

%S 0,1,8,69,712,8705,123456,1994293,36163184,727518177,16081980760,

%T 387499155461,10108673620728,283851555270049,8536572699232592,

%U 273759055527114165,9325469762472018016,336282091434597013313,12797935594025234906664,512609204063389138693957

%N Expansion of e.g.f. exp(x)*(1-x)*x/(1-2*x)^2.

%H Alois P. Heinz, <a href="/A327606/b327606.txt">Table of n, a(n) for n = 0..402</a>

%F E.g.f: exp(x)*(1-x)*x/(1-2*x)^2.

%F a(n) = Sum_{k=1..n} k * A326659(n,k).

%F a(n) ~ n! * exp(1/2) * n * 2^(n-2). - _Vaclav Kotesovec_, Sep 19 2019

%p a:= n-> n!*coeff(series(exp(x)*(1-x)*x/(1-2*x)^2, x, n+1), x, n):

%p seq(a(n), n=0..23);

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n<3, n^3,

%p       2*(n+2)*a(n-1)-(4*n-1)*a(n-2)+2*(n-2)*a(n-3))

%p     end:

%p seq(a(n), n=0..23);

%t With[{nn=20},CoefficientList[Series[Exp[x](1-x)(x/(1-2x)^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 15 2020 *)

%Y Cf. A308876, A326659.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 18 2019