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Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.
6

%I #23 Aug 29 2022 19:47:09

%S 1,1,1,1,2,1,1,3,9,1,1,4,36,64,1,1,5,100,1000,625,1,1,6,225,8000,

%T 50625,7776,1,1,7,441,42875,1500625,4084101,117649,1,1,8,784,175616,

%U 24010000,550731776,481890304,2097152,1,1,9,1296,592704,252047376,31757969376,351298031616,78364164096,43046721,1

%N Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.

%C Maximal term in row n is asymptotically in position k = r*n, where r = A220359 = 0.70350607643... is a root of the equation (1-r)^(2*r-1) = r^(2*r). - _Vaclav Kotesovec_, Nov 15 2012

%H Paul D. Hanna, <a href="/A219206/b219206.txt">Rows n = 0..45, flattened.</a>

%F Row sums equal A167008.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 3, 9, 1;

%e 1, 4, 36, 64, 1;

%e 1, 5, 100, 1000, 625, 1;

%e 1, 6, 225, 8000, 50625, 7776, 1;

%e 1, 7, 441, 42875, 1500625, 4084101, 117649, 1;

%e 1, 8, 784, 175616, 24010000, 550731776, 481890304, 2097152, 1;

%e ...

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

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

%o (Haskell)

%o a219206 n k = a219206_tabl !! n !! k

%o a219206_row n = a219206_tabl !! n

%o a219206_tabl = zipWith (zipWith (^)) a007318_tabl a002262_tabl

%o -- _Reinhard Zumkeller_, Feb 27 2015

%Y Cf. A167008 (row sums).

%Y Cf. A002262, A007318, A219207.

%K nonn,tabl

%O 0,5

%A _Paul D. Hanna_, Nov 14 2012