A327606 Expansion of e.g.f. exp(x)*(1-x)*x/(1-2*x)^2.

0, 1, 8, 69, 712, 8705, 123456, 1994293, 36163184, 727518177, 16081980760, 387499155461, 10108673620728, 283851555270049, 8536572699232592, 273759055527114165, 9325469762472018016, 336282091434597013313, 12797935594025234906664, 512609204063389138693957

Offset: 0

Author

Alois P. Heinz, Sep 18 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..402

Crossrefs

Cf. A308876, A326659.

Programs

Maple

a:= n-> n!*coeff(series(exp(x)*(1-x)*x/(1-2*x)^2, x, n+1), x, n):
seq(a(n), n=0..23);
# second Maple program:
a:= proc(n) option remember; `if`(n<3, n^3,
      2*(n+2)*a(n-1)-(4*n-1)*a(n-2)+2*(n-2)*a(n-3))
    end:
seq(a(n), n=0..23);

Mathematica

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 *)

Formula

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

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

a(n) ~ n! * exp(1/2) * n * 2^(n-2). - Vaclav Kotesovec, Sep 19 2019