OFFSET
3,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = A090447(n,3).
a(n) = (n^3*(n-1)^2*(n-2)^1)/(1!*2!*3!) for n >= 3.
From Colin Barker, Jan 21 2013: (Start)
a(n) = (n^6-4*n^5+5*n^4-2*n^3)/12.
G.f.: -x^3*(x^3+17*x^2+33*x+9)/(x-1)^7. (End)
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 04 2021
From Amiram Eldar, Sep 08 2022: (Start)
Sum_{n>=3} 1/a(n) = 207/4 - 9*Pi^2/2 - 6*zeta(3).
Sum_{n>=3} (-1)^(n+1)/a(n) = 165/4 - Pi^2/4 - 48*log(2) - 9*zeta(3)/2. (End)
MAPLE
seq(mul(binomial(n, k), k=1..3), n=3..30); # Zerinvary Lajos, Dec 13 2007
MATHEMATICA
a[n_] := Product[Binomial[n, k], {k, 0, 3}]; Array[a, 30, 3] (* Amiram Eldar, Sep 08 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Dec 23 2003
STATUS
approved