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%I #11 Sep 08 2022 08:46:20
%S 0,11,146,896,3696,11886,32172,76692,165792,331617,622622,1109108,
%T 1889888,3100188,4920888,7589208,11410944,16774359,24165834,34187384,
%U 47576144,65225930,88210980,117811980,155544480,203189805,262828566,336876876,428125376,539781176
%N a(n) = (15*n^2 + 35*n + 16)*Pochhammer(n, 5) / 6!.
%H G. C. Greubel, <a href="/A293610/b293610.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 28 2019: (Start)
%F G.f.: x*(11 + 58*x + 36*x^2) / (1 - x)^8.
%F a(n) = (n*(384 + 1640*n + 2670*n^2 + 2135*n^3 + 891*n^4 + 185*n^5 + 15*n^6)) / 720.
%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 A293610 := n -> (15*n^2 + 35*n + 16)*pochhammer(n,5)/6!:
%p seq(A293610(n), n=0..29);
%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {0,11,146, 896, 3696, 11886, 32172, 76692}, 40] (* or *) a = (1/720)*(384*#1 + 1640*#1^2 + 2670*#1^3 + 2135*#1^4 + 891*#1^5 + 185*#1^6 + 15*#1^7) & ; Table[a[n], {n, 0, 40}]
%t Table[(15*n^2 + 35*n + 16)*Pochhammer[n, 5]/6!, {n, 0, 50}] (* _G. C. Greubel_, Oct 22 2017 *)
%o (PARI) for(n=0,50, print1((15*n^2 + 35*n + 16)*(n+4)*(n+3)*(n+2)*(n+1)*n/6!, ", ")) \\ _G. C. Greubel_, Oct 22 2017
%o (PARI) concat(0, Vec(x*(11 + 58*x + 36*x^2) / (1 - x)^8 + O(x^40))) \\ _Colin Barker_, Jul 28 2019
%o (Magma) [(15*n^2 + 35*n + 16)*(n+4)*(n+3)*(n+2)*(n+1)*n/Factorial(6):n in [0..50]]; // _G. C. Greubel_, Oct 22 2017
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Oct 13 2017
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