A209427 - OEIS

%I #16 Jan 03 2018 21:58:10

%S 1,1,1,1,4,1,1,27,27,1,1,256,1296,256,1,1,3125,100000,100000,3125,1,1,

%T 46656,11390625,64000000,11390625,46656,1,1,823543,1801088541,

%U 64339296875,64339296875,1801088541,823543,1,1,16777216,377801998336,96717311574016,576480100000000,96717311574016,377801998336,16777216,1

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

%C Row sums equals A167010.

%C Column 1 forms A000312.

%C Antidiagonal sums form A209428.

%H Paul D. Hanna, <a href="/A209427/b209427.txt">Rows n = 0..30, flattened.</a>

%e This triangle begins:

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 27, 27, 1;

%e 1, 256, 1296, 256, 1;

%e 1, 3125, 100000, 100000, 3125, 1;

%e 1, 46656, 11390625, 64000000, 11390625, 46656, 1;

%e 1, 823543, 1801088541, 64339296875, 64339296875, 1801088541, 823543, 1;

%e 1, 16777216, 377801998336, 96717311574016, 576480100000000, 96717311574016, 377801998336, 16777216, 1; ...

%t Table[Binomial[n,k]^n, {n,0,10}, {k,0,n}]// Flatten (* _G. C. Greubel_, Jan 03 2018 *)

%o (PARI) {T(n,k)=binomial(n,k)^n}

%o for(n=0,10,for(k=0,n,print1(T(n,k),","));print(""))

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

%K nonn,tabl

%O 0,5

%A _Paul D. Hanna_, Mar 08 2012