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Fifth column of triangle A075497.
4

%I #8 Jan 01 2018 04:22:16

%S 1,30,560,8400,111216,1360800,15790720,176563200,1922176256,

%T 20518417920,215825326080,2244998246400,23153670762496,

%U 237224718704640,2418102840688640,24549985173504000,248464183682727936

%N Fifth column of triangle A075497.

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

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

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

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

%F 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!.

%Y Cf. A025966, A075511.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002