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A075911 Third column of triangle A075500. 7

%I

%S 1,30,625,11250,188125,3018750,47265625,728906250,11133203125,

%T 168996093750,2554931640625,38523925781250,579858642578125,

%U 8717878417968750,130968170166015625,1966522521972656250,29517837677001953125,442967564392089843750,6646513462066650390625

%N Third column of triangle A075500.

%C The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(5*(m+1)*x)/2!.

%H Colin Barker, <a href="/A075911/b075911.txt">Table of n, a(n) for n = 0..849</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (30,-275,750).

%F a(n) = A075500(n+3, 3) = (5^n)*S2(n+3, 3) with S2(n, m) = A008277(n, m) (Stirling2).

%F a(n) = (5^n - 8*10^n + 9*15^n)/2.

%F G.f.: 1/Product_{k=1..3} (1 - 5*k*x).

%F E.g.f.: (d^3/dx^3)(((exp(5*x)-1)/5)^3)/3! = (exp(5*x) - 8*exp(10*x) + 9*exp(15*x))/2!.

%F a(n) = 30*a(n-1) - 275*a(n-2) + 750*a(n-3) for n > 2. - _Colin Barker_, Dec 11 2015

%t LinearRecurrence[{30,-275,750},{1,30,625},30] (* _Harvey P. Dale_, Oct 06 2017 *)

%o (PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)) + O(x^30)) \\ _Colin Barker_, Dec 11 2015

%Y Cf. A016164, A075912.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002

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Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)