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 A177456 #18 May 01 2024 09:01:55
%S A177456 2,42,1092,35420,1391280,64425438,3442573064,208710267480,
%T A177456 14162980464360,1063958304188780,87677864005521636,
%U A177456 7865449972066576656,763126447532235966816,79629871834780293333510
%N A177456 a(n) = binomial(n^2,n+1)/n.
%C A177456 n divides binomial(n^2,n+1).
%C A177456 Proof 1 :(n+1)*binomial(n^2,n+1) = n*(n-1)*binomial(n^2,n) => n divide binomial(n^2,n+1) because gcd(n,n+1) = 1.
%C A177456 Proof 2 : a(n) = binomial(n^2,n+1)/n = (n-1)*binomial(n^2-2,n-1)=> a(n) is an integer. - _Michel Lagneau_, May 13 2010
%H A177456 G. C. Greubel, <a href="/A177456/b177456.txt">Table of n, a(n) for n = 2..335</a>
%H A177456 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A177456 Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Barry/barry84.html">A Catalan Transform and Related Transformations on Integer Sequences</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%H A177456 Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Barry/barry91.html">On Integer-Sequence-Based Constructions of Generalized Pascal Triangles</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
%F A177456 a(n) = binomial(n^2,n+1)/n.
%F A177456 From _G. C. Greubel_, Apr 29 2024: (Start)
%F A177456 a(n) = (n-1)*A177234(n).
%F A177456 a(n) = (n-1)*A177788(n)/n.
%F A177456 a(n) = n*(n-1)*A177784(n).
%F A177456 a(n) = A014062(n)/n. (End)
%e A177456 For n=4, 1092 is in the sequence because binomial(16,5)/4 = 4368/4 = 1092.
%p A177456 with(numtheory):n0:=30:T:=array(1..n0-1):for n from 2 to n0 do:T[n-1]:= (binomial(n*n,n+1))/n:od:print(T):
%t A177456 Table[Binomial[n^2,n+1]/n, {n,2,30}] (* _G. C. Greubel_, Apr 29 2024 *)
%o A177456 (Magma) [Binomial(n^2,n+1)/n: n in [2..30]]; // _G. C. Greubel_, Apr 29 2024
%o A177456 (SageMath) [binomial(n^2,n+1)/n for n in range(2,31)] # _G. C. Greubel_, Apr 29 2024
%Y A177456 Cf. A000984, A014062, A060545, A177234, A177784, A177788.
%K A177456 nonn
%O A177456 2,1
%A A177456 _Michel Lagneau_, May 09 2010