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 A132202 #19 Oct 21 2023 04:14:15
%S A132202 1,1860,90291600,31082452632000,46764764308702440000,
%T A132202 229747284991066934931840000,3031982831164890119435183865600000,
%U A132202 93453554057243260025029337978773248000000,6055976192395031960092036887782708145734400000000,760152286561053082358524425840024164536832608896000000000
%N A132202 Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3.
%D A132202 Shanzhen Gao and Kenneth Matheis, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.
%H A132202 G. C. Greubel, <a href="/A132202/b132202.txt">Table of n, a(n) for n = 1..85</a>
%F A132202 a(n) = f(3*n, 2*n), where f(m, n) = 2^(-m) * Sum_{j=0..n} (-1)^j*n!*m!*(2*m-2*j)!/(j!*(m-j)!*(n-j)!*6^(n-j)).
%F A132202 From _G. C. Greubel_, Oct 12 2023: (Start)
%F A132202 a(n) = ((6*n)!/(288)^n)*Sum_{j=0..2*n} b(2*n,j)*b(3*n,j)*(-6)^j/(j!*b(2*j, j)*b(6*n,2*j)), where b(x,y) = binomomial(x,y).
%F A132202 a(n) = (6*n)!/(288)^n * Hypergeometric1F1([-2*n], [1/2-3*n], -3/2). (End)
%F A132202 a(n) ~ sqrt(Pi) * 2^(n+1) * 3^(4*n + 1/2) * n^(6*n + 1/2) / exp(6*n+1). - _Vaclav Kotesovec_, Oct 21 2023
%e A132202 1 for 3X2:
%e A132202 11
%e A132202 11
%e A132202 11
%e A132202 1860 for 6X4.
%e A132202 90291600 for 9X6.
%p A132202 f:=proc(m,n) 2^(-m)*add( ((-1)^(i)*m!*n!*(2*m-2*i)!)/ (i!*(m-i)!*(n-i)!*6^(n-i)), i=0..n); end;
%p A132202 [seq(f(3*n,2*n),n=0..10)];
%t A132202 Table[((6*n)!/(288)^n)*Hypergeometric1F1[-2*n,1/2-3*n,-3/2], {n,30}] (* _G. C. Greubel_, Oct 12 2023 *)
%o A132202 (Magma)
%o A132202 B:=Binomial;
%o A132202 A132202:= func< n | Factorial(6*n)/(288)^n*(&+[B(2*n,j)*B(3*n,j)*(-6)^j/(Factorial(j)*B(2*j,j)*B(6*n,2*j)): j in [0..2*n]]) >;
%o A132202 [A132202(n): n in [1..30]]; // _G. C. Greubel_, Oct 12 2023
%o A132202 (SageMath)
%o A132202 b=binomial
%o A132202 def A132202(n): return factorial(6*n)/(288)^n *simplify(hypergeometric([-2*n], [1/2-3*n], -3/2))
%o A132202 [A132202(n) for n in range(1,31)] # _G. C. Greubel_, Oct 12 2023
%Y A132202 Cf. A134648, A134772.
%K A132202 nonn,easy
%O A132202 1,2
%A A132202 _Shanzhen Gao_, Nov 05 2007
%E A132202 Edited and extended with Maple code by _R. H. Hardin_ and _N. J. A. Sloane_, Oct 18 2009