A140805 Triangle T(n, k) read by rows T(n,k) = binomial(n, k)^binomial(n, k).

1, 1, 1, 1, 4, 1, 1, 27, 27, 1, 1, 256, 46656, 256, 1, 1, 3125, 10000000000, 10000000000, 3125, 1, 1, 46656, 437893890380859375, 104857600000000000000000000, 437893890380859375, 46656, 1, 1, 823543, 5842587018385982521381124421

Offset

1,5

Comments

Sequence of coefficients inspired by the Belyi transform: x'->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n).

Row sums are: 1, 2, 6, 56, 47170, 20000006252, 104857600875787780761812064, ...

These symmetrical coefficients remind one of Calabi-Yau base Hodge Diamond matrices. These numbers get large very fast.

References

Leila Schneps (editor), The Grothendieck Theory of Dessins D'enfants, London Mathematical Society, Cambridge Press, page 49.

Links

Table of n, a(n) for n=1..31.

Formula

T(n,k) = binomial(n, k)^binomial(n, k).

Example

{1},
{1, 1},
{1, 4, 1},
{1, 27, 27, 1},
{1, 256, 46656, 256, 1},
{1, 3125, 10000000000, 10000000000, 3125, 1},

Mathematica

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]

Crossrefs

Cf. A007318.

Sequence in context: A088158 A136449 A209427 * A113370 A078536 A173918

Adjacent sequences: A140802 A140803 A140804 * A140806 A140807 A140808

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Jul 15 2008

Status

approved