A075510 Fifth column of triangle A075497.

1, 30, 560, 8400, 111216, 1360800, 15790720, 176563200, 1922176256, 20518417920, 215825326080, 2244998246400, 23153670762496, 237224718704640, 2418102840688640, 24549985173504000, 248464183682727936

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(2*(m+1)*x)/4!.

Crossrefs

Cf. A025966, A075511.

Formula

a(n) = A075497(n+5, 5) = (2^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (2^n - 64*4^n + 486*6^n - 1024*8^n + 625*10^n)/4!.

G.f.: 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)*(1-10*x)).

E.g.f.: (d^5/dx^5)(((exp(2*x)-1)/2)^5)/5! = (exp(2*x) - 64*exp(4*x) + 486*exp(6*x) - 1024*exp(8*x) + 625*exp(10*x))/4!.