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A219206
Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.
6
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
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).
Sequence in context: A293908 A346249 A235453 * A077385 A337219 A220898
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 14 2012
STATUS
approved