A104881 Triangle T(n,k) = Sum_{j=0..k} (n-k)^(k-j), read by rows.
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 15, 5, 1, 1, 6, 21, 40, 31, 6, 1, 1, 7, 31, 85, 121, 63, 7, 1, 1, 8, 43, 156, 341, 364, 127, 8, 1, 1, 9, 57, 259, 781, 1365, 1093, 255, 9, 1, 1, 10, 73, 400, 1555, 3906, 5461, 3280, 511, 10, 1, 1, 11, 91, 585, 2801, 9331, 19531, 21845, 9841, 1023, 11, 1
Offset: 0
Examples
Triangle begins as: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 4, 7, 4, 1; 1, 5, 13, 15, 5, 1;
Links
- G. C. Greubel, Rows n = 0..50 of the triangle, flattened
Programs
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Magma
[(&+[ (n-k)^(k-j): j in [0..k]]): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 15 2021
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Mathematica
T[n_, k_]:= If[k==n, 1, Sum[(n-k)^(k-j), {j,0,k}]]; Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Jun 15 2021 *) -
Sage
flatten([[sum((n-k)^(k-j) for j in (0..k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 15 2021
Comments