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A011935 a(n) = floor( n*(n-1)*(n-2)*(n-3)/25 ).

%I A011935 #24 Aug 03 2025 03:35:19
%S A011935 0,0,0,0,0,4,14,33,67,120,201,316,475,686,960,1310,1747,2284,2937,
%T A011935 3720,4651,5745,7022,8500,10200,12144,14352,16848,19656,22800,26308,
%U A011935 30206,34521,39283,44520,50265,56548,63403,70862,78960,87734,97219,107452,118473
%N A011935 a(n) = floor( n*(n-1)*(n-2)*(n-3)/25 ).
%H A011935 G. C. Greubel, <a href="/A011935/b011935.txt">Table of n, a(n) for n = 0..2500</a>
%H A011935 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1).
%F A011935 a(n) = +4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +a(n-25) -4*a(n-26) +6*a(n-27) -4*a(n-28) +a(n-29). - _R. J. Mathar_, Apr 15 2010
%F A011935 G.f.: x^5*(4 -2*x +x^2 +3*x^3 -2*x^4 +5*x^5 -3*x^6 +4*x^7 -2*x^8 +3*x^9 +2*x^10 -2*x^11 +2*x^12 +3*x^13 -2*x^14 +4*x^15 -3*x^16 +5*x^17 -2*x^18 +3*x^19 +x^20 -2*x^21 +4*x^22)/((1-x)^4*(1-x^25)). - _G. C. Greubel_, Nov 02 2024
%t A011935 Floor[24*Binomial[Range[0,80], 4]/25] (* _G. C. Greubel_, Nov 02 2024 *)
%t A011935 Table[Floor[Times@@(n-Range[0,3])/25],{n,0,40}]  (* or *) LinearRecurrence[{4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1},{0,0,0,0,0,4,14,33,67,120,201,316,475,686,960,1310,1747,2284,2937,3720,4651,5745,7022,8500,10200,12144,14352,16848,19656},40] (* _Harvey P. Dale_, Jan 18 2025 *)
%o A011935 (Magma) [Floor(24*Binomial(n,4)/25): n in [0..80]]; // _G. C. Greubel_, Nov 02 2024
%o A011935 (SageMath) [24*binomial(n,4)//25 for n in range(81)] # _G. C. Greubel_, Nov 02 2024
%Y A011935 Cf. A011915.
%K A011935 nonn,easy
%O A011935 0,6
%A A011935 _N. J. A. Sloane_