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A219207 Triangle, read by rows, where T(n,k) = binomial(n,k)^(k+1) for n>=0, k=0..n. 4
1, 1, 1, 1, 4, 1, 1, 9, 27, 1, 1, 16, 216, 256, 1, 1, 25, 1000, 10000, 3125, 1, 1, 36, 3375, 160000, 759375, 46656, 1, 1, 49, 9261, 1500625, 52521875, 85766121, 823543, 1, 1, 64, 21952, 9834496, 1680700000, 30840979456, 13492928512, 16777216, 1, 1, 81, 46656 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Maximal term in row n is asymptotically in position k = r*n, where r = 0.70350607643... is a root of the equation (1-r)^(2*r-1) = r^(2*r). - Vaclav Kotesovec, Nov 15 2012

The matrix inverse starts

1;

-1,1;

3,-4,1;

-73,99,-27,1;

18055,-24496,6696,-256,1;

-55694851,75563975,-20656000,790000,-3125,1; - R. J. Mathar, Mar 22 2013

LINKS

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

FORMULA

Row sums equal A184731.

EXAMPLE

Triangle of coefficients C(n,k)^(k+1) begins:

1;

1, 1;

1, 4, 1;

1, 9, 27, 1;

1, 16, 216, 256, 1;

1, 25, 1000, 10000, 3125, 1;

1, 36, 3375, 160000, 759375, 46656, 1;

1, 49, 9261, 1500625, 52521875, 85766121, 823543, 1;

1, 64, 21952, 9834496, 1680700000, 30840979456, 13492928512, 16777216, 1; ...

MATHEMATICA

Table[Binomial[n, k]^(k+1), {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Aug 15 2016 *)

PROG

(PARI) {T(n, k)=binomial(n, k)^(k+1)}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A184731, A219206, A184730.

Sequence in context: A299427 A126062 A243608 * A157108 A056647 A056057

Adjacent sequences:  A219204 A219205 A219206 * A219208 A219209 A219210

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Nov 14 2012

STATUS

approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)