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

0,5

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

Links

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

Formula

Row sums equal A167008.

Example

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;
  ...

Prog

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

Crossrefs

Cf. A167008 (row sums).

Cf. A002262, A007318, A219207.

Sequence in context: A293908 A346249 A235453 * A077385 A337219 A220898

Adjacent sequences: A219203 A219204 A219205 * A219207 A219208 A219209

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 14 2012

Status

approved