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a(n) = floor(n(n-1)(n-2)(n-3)/19).
1

%I #16 Oct 18 2022 15:29:00

%S 0,0,0,0,1,6,18,44,88,159,265,416,625,903,1264,1724,2298,3006,3865,

%T 4896,6120,7560,9240,11185,13422,15978,18884,22168,25863,30001,34616,

%U 39745,45423,51688,58580,66138,74406,83425,93240,103896,115440,127920,141385

%N a(n) = floor(n(n-1)(n-2)(n-3)/19).

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 6, -4, 1).

%F From _Chai Wah Wu_, Aug 02 2020: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-19) - 4*a(n-20) + 6*a(n-21) - 4*a(n-22) + a(n-23) for n > 22.

%F G.f.: x^4*(x^2 + 1)^2*(-x^14 - 2*x^13 + 2*x^12 - 3*x^9 - x^8 + 4*x^7 - x^6 - 3*x^5 + 2*x^2 - 2*x - 1)/(x^23 - 4*x^22 + 6*x^21 - 4*x^20 + x^19 - x^4 + 4*x^3 - 6*x^2 + 4*x - 1). (End)

%t Table[Floor[n(n - 1)(n - 2)(n - 3)/19], {n, 0, 50}] (* _Stefan Steinerberger_, Apr 10 2006 *)

%o (PARI) a(n)=n*(n-1)*(n-2)*(n-3)\19 \\ _Charles R Greathouse IV_, Oct 18 2022

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_

%E More terms from _Stefan Steinerberger_, Apr 10 2006