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%I #17 Jun 12 2023 09:26:47
%S 1,1,1,1,4,1,1,9,27,1,1,16,216,256,1,1,25,1000,10000,3125,1,1,36,3375,
%T 160000,759375,46656,1,1,49,9261,1500625,52521875,85766121,823543,1,1,
%U 64,21952,9834496,1680700000,30840979456,13492928512,16777216,1,1,81,46656
%N Triangle, read by rows, where T(n,k) = binomial(n,k)^(k+1) 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="/A219207/b219207.txt">Rows n = 0..45, flattened.</a>
%F Row sums equal A184731.
%e Triangle of coefficients C(n,k)^(k+1) begins:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 9, 27, 1;
%e 1, 16, 216, 256, 1;
%e 1, 25, 1000, 10000, 3125, 1;
%e 1, 36, 3375, 160000, 759375, 46656, 1;
%e 1, 49, 9261, 1500625, 52521875, 85766121, 823543, 1;
%e 1, 64, 21952, 9834496, 1680700000, 30840979456, 13492928512, 16777216, 1; ...
%e MATRIX INVERSE.
%e The matrix inverse starts
%e 1;
%e -1,1;
%e 3,-4,1;
%e -73,99,-27,1;
%e 18055,-24496,6696,-256,1;
%e -55694851,75563975,-20656000,790000,-3125,1; - _R. J. Mathar_, Mar 22 2013
%t Table[Binomial[n,k]^(k+1),{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Aug 15 2016 *)
%o (PARI) {T(n,k)=binomial(n,k)^(k+1)}
%o for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))
%Y Cf. A184731, A219206, A184730.
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Nov 14 2012
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