A209427 T(n,k) = binomial(n,k)^n.

1, 1, 1, 1, 4, 1, 1, 27, 27, 1, 1, 256, 1296, 256, 1, 1, 3125, 100000, 100000, 3125, 1, 1, 46656, 11390625, 64000000, 11390625, 46656, 1, 1, 823543, 1801088541, 64339296875, 64339296875, 1801088541, 823543, 1, 1, 16777216, 377801998336, 96717311574016, 576480100000000, 96717311574016, 377801998336, 16777216, 1

Offset

0,5

Comments

Row sums equals A167010.

Column 1 forms A000312.

Antidiagonal sums form A209428.

Links

Paul D. Hanna, Rows n = 0..30, flattened.

Example

This triangle begins:
1;
1, 1;
1, 4, 1;
1, 27, 27, 1;
1, 256, 1296, 256, 1;
1, 3125, 100000, 100000, 3125, 1;
1, 46656, 11390625, 64000000, 11390625, 46656, 1;
1, 823543, 1801088541, 64339296875, 64339296875, 1801088541, 823543, 1;
1, 16777216, 377801998336, 96717311574016, 576480100000000, 96717311574016, 377801998336, 16777216, 1; ...

Mathematica

Table[Binomial[n, k]^n, {n, 0, 10}, {k, 0, n}]// Flatten (* G. C. Greubel, Jan 03 2018 *)

Prog

(PARI) {T(n, k)=binomial(n, k)^n}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A167010 (row sums), A000312 (column 1), A209428.

Sequence in context: A357744 A088158 A136449 * A140805 A113370 A078536

Adjacent sequences: A209424 A209425 A209426 * A209428 A209429 A209430

Keyword

nonn,tabl

Author

Paul D. Hanna, Mar 08 2012

Status

approved