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

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, 50625, 7776, 1, 1, 7, 441, 42875, 1500625, 4084101, 117649, 1, 1, 8, 784, 175616, 24010000, 550731776, 481890304, 2097152, 1, 1, 9, 1296, 592704, 252047376, 31757969376, 351298031616, 78364164096, 43046721, 1

Offset: 0

Author

Paul D. Hanna, Nov 14 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle begins:
  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,    50625,      7776,         1;
  1, 7, 441,  42875,  1500625,   4084101,    117649,       1;
  1, 8, 784, 175616, 24010000, 550731776, 481890304, 2097152,  1;
  ...
		

Links

• Paul D. Hanna, Rows n = 0..45, flattened.

Crossrefs

Cf. A167008 (row sums).

Cf. A002262, A007318, A219207.

Programs

Haskell

a219206 n k = a219206_tabl !! n !! k
a219206_row n = a219206_tabl !! n
a219206_tabl = zipWith (zipWith (^)) a007318_tabl a002262_tabl
-- Reinhard Zumkeller, Feb 27 2015

PARI

{T(n,k)=binomial(n,k)^k}
for(n=0,10,for(k=0,n,print1(T(n,k),", "));print(""))

Formula

Row sums equal A167008.