This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288689 #7 Aug 18 2025 18:31:43
%S A288689 1,1,6,46,376,2841,19718,128535,805848,4942711,29970542,180700389,
%T A288689 1086570460,6525662885,39170135870,235062159691,1410477973872,
%U A288689 8463133736523,50779476069198,304678570340665,1828075815690100,10968466276145161,65810827526263678
%N A288689 Number of n-digit biquanimous strings using digits {0,1,...,5}.
%C A288689 A biquanimous string is a string whose digits can be split into two groups with equal sums.
%H A288689 Alois P. Heinz, <a href="/A288689/b288689.txt">Table of n, a(n) for n = 0..1000</a>
%H A288689 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (23, -231, 1351, -5153, 13557, -25301, 33829, -32226, 21368, -9376, 2448, -288).
%F A288689 G.f.: (144*x^14 -1224*x^13 +4976*x^12 -11002*x^11 +18115*x^10 -25255*x^9 +30319*x^8 -29516*x^7 +21747*x^6 -11691*x^5 +4506*x^4 -1212*x^3 +214*x^2 -22*x +1) / ((6*x-1) *(3*x-1) *(2*x-1)^4 *(x-1)^6).
%t A288689 CoefficientList[Series[(144x^14-1224x^13+4976x^12-11002x^11+18115x^10-25255x^9+30319x^8-29516x^7+21747x^6-11691x^5+4506x^4-1212x^3+214x^2-22x+1)/((6x-1)(3x-1)(2x-1)^4(x-1)^6),{x,0,40}],x] (* or *) LinearRecurrence[{23,-231,1351,-5153,13557,-25301,33829,-32226,21368,-9376,2448,-288},{1,1,6,46,376,2841,19718,128535,805848,4942711,29970542,180700389,1086570460,6525662885,39170135870},40] (* _Harvey P. Dale_, Aug 18 2025 *)
%Y A288689 Column k=5 of A288638.
%K A288689 nonn,easy
%O A288689 0,3
%A A288689 _Alois P. Heinz_, Jun 13 2017