OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Riemann Tensor
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(2) = 1, otherwise a(n) = n*(n-1)*(n-2)*(n+3)/12 = A005701(n-3).
From Chai Wah Wu, Aug 31 2016: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.
G.f.: x^2*(x^5 - 5*x^4 + 10*x^3 - 9*x^2 + 2*x - 1)/(x - 1)^5. (End)
MATHEMATICA
CoefficientList[Series[x^2*(x^5 - 5*x^4 + 10*x^3 - 9*x^2 + 2*x - 1)/(x - 1)^5, {x, 0, 50}], x] (* G. C. Greubel, May 12 2017 *)
Join[{0, 1}, Table[n (n - 1) (n - 2) (n + 3) / 12, {n, 3, 40}]] (* Vincenzo Librandi, May 13 2017 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec(x^2*(x^5-5*x^4+10*x^3-9*x^2+2*x-1)/(x-1)^5)) \\ G. C. Greubel, May 12 2017
(Magma) [0, 1] cat [n*(n-1)*(n-2)*(n+3)/12: n in [3..60]]; // Vincenzo Librandi, May 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved