A034866 a(n) = n!*(n-4)/2, n > 4, and a(4) = 4.

4, 60, 720, 7560, 80640, 907200, 10886400, 139708800, 1916006400, 28021593600, 435891456000, 7192209024000, 125536739328000, 2311968282624000, 44816615940096000, 912338253066240000

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 4..445
• J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
• Index entries for sequences related to factorial numbers

Programs

GAP

A034866:=Concatenation([4],List([5..20],n->Factorial(n)*(n-4)/2)); # Muniru A Asiru, Feb 17 2018

Magma

[4] cat [Factorial(n)*(n-4)/2: n in [5..30]]; // G. C. Greubel, Feb 16 2018

Maple

[4,seq(factorial(n)*(n-4)/2,n=5..20)]; # Muniru A Asiru, Feb 17 2018

Mathematica

Join[{4}, Table[n!*(n-4)/2, {n,5,30}]] (* or *) Drop[With[{nn = 30}, CoefficientList[Series[x^4*(1 + x + x^2)/(6*(1 - x)^2), {x, 0, nn}], x]*Range[0, nn]!], 4]  (* G. C. Greubel, Feb 16 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(x^4*(1+x+x^2)/(6*(1-x)^2))) \\ G. C. Greubel, Feb 16 2018

Formula

a(n) = A034865(n), n > 4. - R. J. Mathar, Oct 20 2008

(-n+5)*a(n) + n*(n-4)*a(n-1) = 0. - R. J. Mathar, Apr 03 2017

E.g.f.: x^4*(1 + x + x^2)/(6*(1 - x)^2). - G. C. Greubel, Feb 16 2018