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 A215546 #13 Aug 29 2025 04:13:45
%S A215546 0,132,9996,92092,451269,1570800,4395118,10559208,22664655,44602348,
%T A215546 81921840,142247364,235740505,375609528,578665362,865924240,
%U A215546 1263256995,1802085012,2520122836,3462167436,4680934125,6237939136,8204428854,10662355704,13705400695
%N A215546 Number of standard Young tableaux of shape [6n,6].
%C A215546 Also the number of binary words with 6n 1's and 6 0's such that for every prefix the number of 1's is >= the number of 0's.
%H A215546 Alois P. Heinz, <a href="/A215546/b215546.txt">Table of n, a(n) for n = 0..1000</a>
%H A215546 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>.
%F A215546 G.f.: (5*x^6-35*x^5-609*x^4-11921*x^3-24892*x^2-9072*x-132)*x/(x-1)^7.
%F A215546 a(n) = (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10 for n>0, a(0) = 0.
%F A215546 Sum_{n>=1} 1/a(n) = 76/385 - 1559*Pi/(924*sqrt(3)) + 2080*log(2)/231 - 135*log(3)/44. - _Amiram Eldar_, Aug 29 2025
%p A215546 a:= n-> max(0, (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10):
%p A215546 seq(a(n), n=0..40);
%Y A215546 Row n=6 of A214776.
%K A215546 nonn,changed
%O A215546 0,2
%A A215546 _Alois P. Heinz_, Aug 16 2012