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A075914 Sixth column of triangle A075500. 3

%I

%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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Last modified March 28 12:57 EDT 2020. Contains 333085 sequences. (Running on oeis4.)