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 A110537 Symmetric number square associated to ceiling(k^n/n^k), read by antidiagonals. 4
 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, 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, 47, 40, 47, 35, 12, 1, 1, 18, 72, 102, 79, 81, 81, 79, 102, 72, 18, 1, 1, 30, 152, 237, 183, 168 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums of triangle are A110538. Diagonal sums are A110539. The row sums of the inverse of the triangle may be A000007. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA Number square T(n, k) = Sum_{j=1..min(n, k)} ceiling(j^n/n^j)*ceiling(j^k/k^j). 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). EXAMPLE As a number square, rows begin 1,1,1,1,1,1,1,... 1,2,2,2,3,3,4,... 1,2,3,4,5,7,11,... 1,2,4,7,9,15,25,... 1,3,5,9,14,24,40,... 1,3,7,15,24,47,81,... As a number triangle, rows begin 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; MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A204026 A300119 A323211 * A144434 A322057 A323767 Adjacent sequences:  A110534 A110535 A110536 * A110538 A110539 A110540 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Jul 25 2005 STATUS approved

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)