OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
From Colin Barker, Jul 28 2019: (Start)
G.f.: x*(11 + 58*x + 36*x^2) / (1 - x)^8.
a(n) = (n*(384 + 1640*n + 2670*n^2 + 2135*n^3 + 891*n^4 + 185*n^5 + 15*n^6)) / 720.
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.
(End)
MATHEMATICA
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}]
Table[(15*n^2 + 35*n + 16)*Pochhammer[n, 5]/6!, {n, 0, 50}] (* G. C. Greubel, Oct 22 2017 *)
PROG
(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
(PARI) concat(0, Vec(x*(11 + 58*x + 36*x^2) / (1 - x)^8 + O(x^40))) \\ Colin Barker, Jul 28 2019
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 13 2017
STATUS
approved