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Sixth column of triangle A075497.
3

%I #8 Jan 01 2018 04:23:13

%S 1,42,1064,21168,365232,5743584,84713728,1193127936,16239711488,

%T 215394955776,2800564795392,35851775791104,453374980255744,

%U 5677724481773568,70550796621971456,871159544637161472

%N Sixth column of triangle A075497.

%C The e.g.f. given below is Sum_{m=0..5} A075513(6,m)*exp(2*(m+1)*x)/5!.

%F a(n) = A075497(n+6, 6) = (2^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

%F a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*2)^n/5!.

%F G.f.: 1/Product_{k=1..6} (1 - 2*k*x).

%F E.g.f.: (d^6/dx^6)(((exp(2*x)-1)/2)^6)/6! = (-exp(2*x) + 160*exp(4*x) - 2430*exp(6*x) + 10240*exp(8*x) - 15625*exp(10*x) + 7776*exp(12*x))/5!.

%Y Cf. A075510, A075512.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002