OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014 (page 16).
Richard P. Brent, Generalising Tuenter's binomial sums, Journal of Integer Sequences, 18 (2015), Article 15.3.2.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)
FORMULA
G.f.: x*(1 + 81*x + 339*x^2 + 155*x^3)/(1 - x)^5.
E.g.f.: x*(1 + 42*x + 84*x^2 + 24*x^3)*exp(x).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
See page 7 in Brent's paper:
A272380(n) = n^2*a(n) - n*(n-1)*a(n-1).
From Peter Bala, Jan 30 2019: (Start)
Let a(n,x) = Product_{k = 0..n} (x - k)/(x + k). Then for positive integer x we have x^2*(24*x^3 - 60*x^2 + 54*x - 17) = Sum_{n >= 0} ((n+1)^9 + n^9)*a(n,x) and x*(24*x^3 - 60*x^2 + 54*x - 17) = Sum_{n >= 0} ((n+1)^8 - n^8)*a(n,x). Both identities are also valid for complex x in the half-plane Re(x) > 9/2. See the Bala link in A036970. Cf. A272378 and A272380. (End)
MATHEMATICA
Table[n (24 n^3 - 60 n^2 + 54 n - 17), {n, 0, 50}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 86, 759, 3100}, 40] (* Harvey P. Dale, Mar 24 2021 *)
PROG
(Magma) [n*(24*n^3 - 60*n^2 + 54*n - 17): n in [0..50]];
(PARI) vector(100, n, n--; n*(24*n^3 - 60*n^2 + 54*n - 17)) \\ Altug Alkan, Apr 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 29 2016
STATUS
approved