%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