A238474 a(n) = (-1)^n*(n+3)!/(2*(n+1)) for n >= 0.

3, -6, 20, -90, 504, -3360, 25920, -226800, 2217600, -23950080, 283046400, -3632428800, 50295168000, -747242496000, 11856247603200, -200074178304000, 3577797070848000, -67580611338240000, 1344498478202880000, -28100018194440192000, 615524208068689920000

Offset: 0

Author

Wolfdieter Lang, Mar 01 2014

Keywords

• sign
• easy

Comments

Third column of Sheffer type triangle A238363 (without leading zeros).

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A238363.

Programs

Mathematica

Fold[Append[#1, (-1)^#2 (#2 + 3)!/(2 (#2 + 1))] &, {3}, Range@ 20] (* Michael De Vlieger, Dec 18 2017 *)

Formula

a(n) = (-1)^n*(n+3)!/(2*(n+1)) for n >= 0.

E.g.f.: (d^3/dx^3)(log(1+x)*x^2/2!) = (x^2+3*x+3)/(1+x)^3.