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A110535
Triangle formed from ceiling(k^n/n^k).
2
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.
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jul 25 2005
STATUS
approved