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A140805 Positive triangular sequence of coefficients inspired by the Belyi transform: x'->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n): t(n,m)=Binomial[n, m]^Binomial[n, m]. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

These symmetrical coefficients remind one of Calbi-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,m)=Binomial[n, m]^Binomial[n, m].

EXAMPLE

{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, 1102507499354148695951786433413508348166942596435546875, 1102507499354148695951786433413508348166942596435546875, 5842587018385982521381124421, 823543, 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

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

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Last modified April 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)