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 A215545 #12 Oct 21 2022 21:38:59 %S A215545 0,42,1638,10659,40480,115101,272272,566618,1072764,1888460,3137706, %T A215545 4973877,7582848,11186119,16043940,22458436,30776732,41394078, %U A215545 54756974,71366295,91780416,116618337,146562808,182363454,224839900,274884896,333467442,401635913 %N A215545 Number of standard Young tableaux of shape [5n,5]. %C A215545 Also the number of binary words with 5n 1's and 5 0's such that for every prefix the number of 1's is >= the number of 0's. %H A215545 Alois P. Heinz, <a href="/A215545/b215545.txt">Table of n, a(n) for n = 0..1000</a> %H A215545 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a> %H A215545 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1). %F A215545 G.f.: (4*x^5-24*x^4+256*x^3+1461*x^2+1386*x+42)*x/(x-1)^6. %F A215545 a(n) = (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24 for n>0, a(0) = 0. %p A215545 a:= n-> max(0, (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24): %p A215545 seq(a(n), n=0..40); %Y A215545 Row n=5 of A214776. %K A215545 nonn,easy %O A215545 0,2 %A A215545 _Alois P. Heinz_, Aug 15 2012