cp's OEIS Frontend

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.

A215548 Number of standard Young tableaux of shape [8n,8].

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%I A215548 #11 Mar 17 2020 17:11:09
%S A215548 0,1430,389367,7152444,58261125,303719922,1188576675,3804949176,
%T A215548 10495906641,25810820750,57928578191,120681823860,236332181085,
%U A215548 439263172458,780774342075,1335176857200,2207407644585,3542395893894,5536432537895,8450810096300,12628017047349
%N A215548 Number of standard Young tableaux of shape [8n,8].
%C A215548 Also the number of binary words with 8n 1's and 8 0's such that for every prefix the number of 1's is >= the number of 0's.
%H A215548 Alois P. Heinz, <a href="/A215548/b215548.txt">Table of n, a(n) for n = 0..1000</a>
%H A215548 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A215548 G.f.: (7*x^8 -63*x^7 -9615*x^6 -572643*x^5 -4331133*x^4 -7786221*x^3 -3699621*x^2 -376497*x -1430)*x / (x-1)^9.
%F A215548 a(n) = C(8*n+8,8)*(8*n-7)/(8*n+1) for n>0, a(0) = 0.
%p A215548 a:= n-> max(0, binomial(8*n+8,8)*(8*n-7)/(8*n+1)):
%p A215548 seq(a(n), n=0..30);
%t A215548 Join[{0},Table[(Binomial[8n+8,8](8n-7))/(8n+1),{n,20}]] (* _Harvey P. Dale_, Mar 17 2020 *)
%Y A215548 Row n=8 of A214776.
%K A215548 nonn
%O A215548 0,2
%A A215548 _Alois P. Heinz_, Aug 16 2012