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A110537 Symmetric number square associated to ceiling(k^n/n^k), read by antidiagonals. 4

%I

%S 1,1,1,1,2,1,1,2,2,1,1,2,3,2,1,1,3,4,4,3,1,1,3,5,7,5,3,1,1,4,7,9,9,7,

%T 4,1,1,5,11,15,14,15,11,5,1,1,8,18,25,24,24,25,18,8,1,1,12,35,47,40,

%U 47,40,47,35,12,1,1,18,72,102,79,81,81,79,102,72,18,1,1,30,152,237,183,168

%N Symmetric number square associated to ceiling(k^n/n^k), read by antidiagonals.

%C Row sums of triangle are A110538. Diagonal sums are A110539. The row sums of the inverse of the triangle may be A000007.

%H G. C. Greubel, <a href="/A110537/b110537.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F Number square T(n, k) = Sum_{j=1..min(n, k)} ceiling(j^n/n^j)*ceiling(j^k/k^j).

%F As a number triangle, T(n, k) = if(k<=n, Sum_{j=1..min(n-k+1, k)} ceiling(j^(n-k+1)/(n-k+1)^j)*ceiling(j^k/k^j), 0).

%e As a number square, rows begin

%e 1,1,1,1,1,1,1,...

%e 1,2,2,2,3,3,4,...

%e 1,2,3,4,5,7,11,...

%e 1,2,4,7,9,15,25,...

%e 1,3,5,9,14,24,40,...

%e 1,3,7,15,24,47,81,...

%e As a number triangle, rows begin

%e 1;

%e 1,1;

%e 1,2,1;

%e 1,2,2,1;

%e 1,2,3,2,1;

%e 1,3,4,4,3,1;

%e 1,3,5,7,5,3,1;

%t T[n_, k_] := If[k <= n, Sum[Ceiling[j^(n - k + 1)/(n - k + 1)^j]*Ceiling[j^k/k^j], {j, 1, Min[n - k + 1, k]}], 0]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Aug 30 2017 *)

%o (PARI) for(n=1,20, for(k=1,n, print1(if(k<=n, sum(j=1,min(n-k+1, k), ceil(j^(n-k+1)/(n-k+1)^j)*ceil(j^k/k^j)), 0), ", "))) \\ _G. C. Greubel_, Aug 30 2017

%K easy,nonn,tabl

%O 1,5

%A _Paul Barry_, Jul 25 2005

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Last modified October 18 03:25 EDT 2021. Contains 348065 sequences. (Running on oeis4.)