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A158117
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Triangle T(n, k) = 10^(k*(n-k)), read by rows.
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14
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1, 1, 1, 1, 10, 1, 1, 100, 100, 1, 1, 1000, 10000, 1000, 1, 1, 10000, 1000000, 1000000, 10000, 1, 1, 100000, 100000000, 1000000000, 100000000, 100000, 1, 1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k, q) = c(n,q)/(c(k,q)*c(n-k,q)) where c(n, k) = binomial(q+2, 2)^binomial(n+1, 2), c(n, 0) = n!, and q = 3.
T(n, k, q) = binomial(q+2, 2)^(k*(n-k)) with q = 3.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 8. - G. C. Greubel, Jun 30 2021
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 10, 1;
1, 100, 100, 1;
1, 1000, 10000, 1000, 1;
1, 10000, 1000000, 1000000, 10000, 1;
1, 100000, 100000000, 1000000000, 100000000, 100000, 1;
1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1;
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MATHEMATICA
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(* First program *)
T[n_, k_, q_]= Binomial[q+2, 2](k*(n-k));
Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)
(* Second program *)
With[{m=8}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
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PROG
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(Magma) [10^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[10^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
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CROSSREFS
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Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), A176642 (m=6), this sequence (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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