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A293613 a(n) = (1/4)*(7*n + 17)*(5*n + 6)*Pochhammer(n, 6) / 6!.

%I A293613 #14 Sep 08 2022 08:46:20
%S A293613 0,66,868,5586,24570,84630,245322,625086,1440582,3063060,6096090,
%T A293613 11479468,20624604,35587188,59283420,95756580,150501204,230852622,
%U A293613 346450104,509782350,736824550,1047776730,1467913590,2028556530,2768179050,3733657200,4981677246,6580313208
%N A293613 a(n) = (1/4)*(7*n + 17)*(5*n + 6)*Pochhammer(n, 6) / 6!.
%H A293613 G. C. Greubel, <a href="/A293613/b293613.txt">Table of n, a(n) for n = 0..1000</a>
%H A293613 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A293613 From _Colin Barker_, Jul 28 2019: (Start)
%F A293613 G.f.: 2*x*(33 + 137*x + 75*x^2) / (1 - x)^9.
%F A293613 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
%F A293613 a(n) = ((n*(12240 + 43188*n + 61948*n^2 + 46835*n^3 + 20200*n^4 + 4982*n^5 + 652*n^6 + 35*n^7))) / 2880.
%F A293613 (End)
%p A293613 A293613 := n -> (1/4)*(7*n + 17)*(5*n + 6)*pochhammer(n,6)/6!;
%p A293613 seq(A293613(n), n=0..29);
%t A293613 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {0, 66, 868, 5586, 24570, 84630, 245322, 625086, 1440582}, 40] (* or *) a = (12240 #1 + 43188 #1^2 + 61948 #1^3 + 46835 #1^4 + 20200 #1^5 + 4982 #1^6 + 652 #1^7 + 35 #1^8)/2880 & ; Table[a[n], {n, 0, 40}]
%t A293613 Table[(7*n + 17)*(5*n + 6)*Pochhammer[n, 6]/(4*6!), {n, 0, 50}] (* _G. C. Greubel_, Oct 23 2017 *)
%o A293613 (PARI) for(n=0,50, print1((7*n + 17)*(5*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(4*6!), ", ")) \\ _G. C. Greubel_, Oct 23 2017
%o A293613 (PARI) concat(0, Vec(2*x*(33 + 137*x + 75*x^2) / (1 - x)^9 + O(x^40))) \\ _Colin Barker_, Jul 28 2019
%o A293613 (Magma) [(7*n + 17)*(5*n + 6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/(4*Factorial(6)): n in [0..50]]; // _G. C. Greubel_, Oct 23 2017
%K A293613 nonn,easy
%O A293613 0,2
%A A293613 _Peter Luschny_, Oct 13 2017