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 A054688 #30 Aug 06 2025 07:48:19
%S A054688 1,1,10,165,3876,118755,4496388,202927725,10639125640,635627275767,
%T A054688 42634215112710,3172596834321200,259398433286078100,
%U A054688 23116565732981832150,2230164446387219893320,231574204669402103059965,25751746463640423324267024,3053419608195531383028424575
%N A054688 Number of nonnegative integer n X n matrices with sum of elements equal to n; polynomial symmetric functions of matrix of order n.
%C A054688 Conjecture: a(n) equals the sum of squares of the number of semistandard Young tableaux over all partitions of n. - _Wouter Meeussen_, Feb 02 2025
%D A054688 E. R. Cavalcanti and M. A. Spohn, On the applicability of mobility metrics for user movement pattern recognition in MANETs, in Proceeding MobiWac '13 Proceedings of the 11th ACM international symposium on Mobility management and wireless access, Pages 123-130, ACM New York, NY, USA 2013, ISBN: 978-1-4503-2355-0 doi:10.1145/2508222.2508228
%H A054688 Alois P. Heinz, <a href="/A054688/b054688.txt">Table of n, a(n) for n = 0..337</a>
%F A054688 a(n) = C(n^2+n-1, n).
%F A054688 a(n) = [x^n] 1/(1 - x)^(n^2). - _Ilya Gutkovskiy_, Oct 03 2017
%F A054688 a(n) ~ exp(n + 1/2) * n^(n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Aug 06 2025
%p A054688 a:= n-> binomial(n*(n+1)-1, n):
%p A054688 seq(a(n), n=0..17); # _Alois P. Heinz_, Oct 22 2021
%t A054688 Table[Binomial[n^2 + n - 1, n], {n, 0, 17}] (* _Michael De Vlieger_, Oct 05 2017 *)
%o A054688 (PARI) a(n) = binomial(n^2+n-1, n); \\ _Altug Alkan_, Oct 03 2017
%Y A054688 Cf. A001700, A007716, A262030.
%K A054688 easy,nonn
%O A054688 0,3
%A A054688 _Vladeta Jovovic_, Apr 19 2000
%E A054688 a(15) corrected by _Ilya Gutkovskiy_, Oct 03 2017