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 A215542 #19 Aug 29 2025 03:55:32
%S A215542 1,5,54,663,8602,115101,1570800,21732542,303719922,4277470470,
%T A215542 60610884906,863102246760,12340998865104,177064708142315,
%U A215542 2547927647834040,36757054103054076,531436857842656610,7698470087956704210,111712846834848074340,1623556455926349703605
%N A215542 a(n) = binomial(6*n,n)*(4*n+1)/(5*n+1).
%C A215542 Number of standard Young tableaux of shape [5n,n].
%H A215542 Alois P. Heinz, <a href="/A215542/b215542.txt">Table of n, a(n) for n = 0..260</a>
%H A215542 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>.
%F A215542 a(n) = C(6*n,n)*(4*n+1)/(5*n+1).
%F A215542 a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(4*n+1). - _Ilya Gutkovskiy_, Nov 01 2017
%F A215542 Recurrence: 5*n*(4*n - 3)*(5*n - 3)*(5*n - 2)*(5*n - 1)*(5*n + 1)*a(n) = 72*(2*n - 1)*(3*n - 2)*(3*n - 1)*(4*n + 1)*(6*n - 5)*(6*n - 1)*a(n-1). - _Vaclav Kotesovec_, Feb 03 2018
%F A215542 a(n) ~ 3^(6*n+1/2) * 4^(3*n+1) / (5^(5*n+3/2) * sqrt(Pi*n)). - _Amiram Eldar_, Aug 29 2025
%p A215542 a:= n-> binomial(6*n,n)*(4*n+1)/(5*n+1):
%p A215542 seq(a(n), n=0..20);
%t A215542 Table[Binomial[6n,n] (4n+1)/(5n+1),{n,0,30}] (* _Harvey P. Dale_, Mar 06 2014 *)
%Y A215542 Column k=5 of A214776.
%K A215542 nonn,changed
%O A215542 0,2
%A A215542 _Alois P. Heinz_, Aug 15 2012