A110535 Triangle formed from ceiling(k^n/n^k).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 4, 3, 1, 1, 3, 7, 7, 5, 3, 1, 1, 4, 13, 16, 12, 7, 3, 1, 1, 7, 27, 40, 34, 19, 9, 4, 1, 1, 11, 60, 105, 98, 61, 29, 11, 4, 1, 1, 17, 134, 287, 304, 205, 102, 41, 14, 4, 1, 1, 29, 308, 810, 982, 729, 387, 160, 55, 17, 5, 1

Offset

0,9

Comments

Correlation matrix is A110537. Row sums are A110536. The row sums of the inverse matrix may be A000007.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

Number triangle T(n, k) = if(k<=n, ceiling(k^n/n^k), 0).

Example

Rows begin
1;
1, 1;
1, 1, 1;
1, 1, 2, 1;
1, 2, 2, 2, 1;
1, 2, 4, 4, 3, 1;
1, 3, 7, 7, 5, 3, 1;
1, 4, 13, 16, 12, 7, 3, 1;

Mathematica

Table[Ceiling[k^n/n^k], {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Aug 30 2017 *)

Prog

(PARI) for(n=1, 20, for(k=1, n, print1(ceil(k^n/n^k), ", "))) \\ G. C. Greubel, Aug 30 2017
(Magma) /* As triangle */ [[Ceiling(k^n/n^k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Aug 30 2017

Crossrefs

Sequence in context: A170906 A123245 A262611 * A033941 A053256 A336498

Adjacent sequences: A110532 A110533 A110534 * A110536 A110537 A110538

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 25 2005

Status

approved