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A219206 Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.

%I A219206 #23 Aug 29 2022 19:47:09
%S A219206 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 A219206 50625,7776,1,1,7,441,42875,1500625,4084101,117649,1,1,8,784,175616,
%U A219206 24010000,550731776,481890304,2097152,1,1,9,1296,592704,252047376,31757969376,351298031616,78364164096,43046721,1
%N A219206 Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.
%C A219206 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 A219206 Paul D. Hanna, <a href="/A219206/b219206.txt">Rows n = 0..45, flattened.</a>
%F A219206 Row sums equal A167008.
%e A219206 Triangle begins:
%e A219206   1;
%e A219206   1, 1;
%e A219206   1, 2,   1;
%e A219206   1, 3,   9,      1;
%e A219206   1, 4,  36,     64,        1;
%e A219206   1, 5, 100,   1000,      625,         1;
%e A219206   1, 6, 225,   8000,    50625,      7776,         1;
%e A219206   1, 7, 441,  42875,  1500625,   4084101,    117649,       1;
%e A219206   1, 8, 784, 175616, 24010000, 550731776, 481890304, 2097152,  1;
%e A219206   ...
%o A219206 (PARI) {T(n,k)=binomial(n,k)^k}
%o A219206 for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%o A219206 (Haskell)
%o A219206 a219206 n k = a219206_tabl !! n !! k
%o A219206 a219206_row n = a219206_tabl !! n
%o A219206 a219206_tabl = zipWith (zipWith (^)) a007318_tabl a002262_tabl
%o A219206 -- _Reinhard Zumkeller_, Feb 27 2015
%Y A219206 Cf. A167008 (row sums).
%Y A219206 Cf. A002262, A007318, A219207.
%K A219206 nonn,tabl
%O A219206 0,5
%A A219206 _Paul D. Hanna_, Nov 14 2012