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%I #12 Sep 08 2022 08:46:20
%S 0,26,238,1176,4200,12180,30492,68376,140712,270270,490490,848848,
%T 1410864,2264808,3527160,5348880,7922544,11490402,16353414,22881320,
%U 31523800,42822780,57425940,76101480,99754200,129442950,166399506,212048928,268031456,336226000
%N a(n) = (8*n + 18)*Pochhammer(n, 6) / 6!.
%H G. C. Greubel, <a href="/A293614/b293614.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F From _Colin Barker_, Jul 29 2019: (Start)
%F G.f.: 2*x*(13 + 15*x) / (1 - x)^8.
%F a(n) = (n*(1080 + 2946*n + 3121*n^2 + 1665*n^3 + 475*n^4 + 69*n^5 + 4*n^6)) / 360.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
%F (End)
%p A293614 := n -> (8*n + 18)*pochhammer(n,6)/6!;
%p seq(A293614(n), n=0..29);
%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {0, 26, 238, 1176, 4200, 12180, 30492, 68376}, 40] (* or *) a = 1/360 (1080 #1 + 2946 #1^2 + 3121 #1^3 + 1665 #1^4 + 475 #1^5 + 69 #1^6 + 4 #1^7) &; Table[a[n], {n, 0, 40}]
%t Table[(8*n + 18)*Pochhammer[n, 6]/6!, {n, 0, 50}] (* _G. C. Greubel_, Oct 23 2017 *)
%o (PARI) for(n=0,50, print1((8*n + 18)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/6!, ", ")) \\ _G. C. Greubel_, Oct 23 2017
%o (PARI) concat(0, Vec(2*x*(13 + 15*x) / (1 - x)^8 + O(x^40))) \\ _Colin Barker_, Jul 29 2019
%o (Magma) [(8*n + 18)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n/Factorial(6): n in [0..50]]; // _G. C. Greubel_, Oct 23 2017
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Oct 13 2017
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