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%I #16 Dec 12 2015 13:13:01
%S 1,105,6650,330750,14266875,560896875,20682062500,728227500000,
%T 24779833203125,821666548828125,26708267167968750,854772944238281250,
%U 27023254648193359375,846046877171630859375,26282219820458984375000,811330550012329101562500
%N Sixth column of triangle A075500.
%C The e.g.f. given below is Sum_{m=0..5}(A075513(6,m)*exp(5*(m+1)*x))/5!.
%H Colin Barker, <a href="/A075914/b075914.txt">Table of n, a(n) for n = 0..675</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (105,-4375,91875,-1015000,5512500,-11250000).
%F a(n) = A075500(n+6, 6) = (5^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)*5)^n)/5!.
%F G.f.: 1/Product_{k=1..6}(1-5*k*x).
%F E.g.f.: (d^6/dx^6)((((exp(5*x)-1)/5)^6)/6!) = (-exp(5*x) + 160*exp(10*x) - 2430*exp(15*x) + 10240*exp(20*x) - 15625*exp(25*x) + 7776*exp(30*x))/5!.
%F G.f.: 1 / ((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)). - _Colin Barker_, Dec 12 2015
%t Table[5^(n-1) * (-1 + 5*2^(5+n) + 5*2^(11+2*n) - 10*3^(5+n) - 5^(6+n) + 6^(5+n))/24, {n, 0, 20}] (* _Vaclav Kotesovec_, Dec 12 2015 *)
%o (PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)) + O(x^30)) \\ _Colin Barker_, Dec 12 2015
%Y Cf. A000351, A016164, A075911, A075912, A075913, A075915.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 02 2002
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