%I #9 Apr 28 2023 12:19:12
%S 1,1,1,1,4,1,1,27,27,1,1,256,46656,256,1,1,3125,10000000000,
%T 10000000000,3125,1,1,46656,437893890380859375,
%U 104857600000000000000000000,437893890380859375,46656,1,1,823543,5842587018385982521381124421
%N Triangle T(n, k) read by rows T(n,k) = binomial(n, k)^binomial(n, k).
%C Sequence of coefficients inspired by the Belyi transform: x'->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n).
%C Row sums are: 1, 2, 6, 56, 47170, 20000006252, 104857600875787780761812064, ...
%C These symmetrical coefficients remind one of Calabi-Yau base Hodge Diamond matrices. These numbers get large very fast.
%D Leila Schneps (editor), The Grothendieck Theory of Dessins D'enfants, London Mathematical Society, Cambridge Press, page 49.
%F T(n,k) = binomial(n, k)^binomial(n, k).
%e {1},
%e {1, 1},
%e {1, 4, 1},
%e {1, 27, 27, 1},
%e {1, 256, 46656, 256, 1},
%e {1, 3125, 10000000000, 10000000000, 3125, 1},
%t Clear[t, n, m, a] t[n_, m_] = Binomial[n, m]^Binomial[n, m]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]
%Y Cf. A007318.
%K nonn,tabl
%O 1,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 15 2008