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 A158116 Triangle T(n,k) = 6^(k*(n-k)), read by rows. 14
 1, 1, 1, 1, 6, 1, 1, 36, 36, 1, 1, 216, 1296, 216, 1, 1, 1296, 46656, 46656, 1296, 1, 1, 7776, 1679616, 10077696, 1679616, 7776, 1, 1, 46656, 60466176, 2176782336, 2176782336, 60466176, 46656, 1, 1, 279936, 2176782336, 470184984576, 2821109907456, 470184984576, 2176782336, 279936, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n,k) = 6^(k*(n-k)). - Tom Edgar, Feb 20 2014 T(n,k) = (1/n)*(6^(n-k)*k*T(n-1,k-1) + 6^k*(n-k)*T(n-1,k)). - Tom Edgar, Feb 20 2014 From G. C. Greubel, Jun 30 2021: (Start) T(n, k, m) = (m+2)^(k*(n-k)) with m = 4. T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 2. (End) EXAMPLE Triangle starts: 1; 1, 1; 1, 6, 1; 1, 36, 36, 1; 1, 216, 1296, 216, 1; 1, 1296, 46656, 46656, 1296, 1; 1, 7776, 1679616, 10077696, 1679616, 7776, 1; 1, 46656, 60466176, 2176782336, 2176782336, 60466176, 46656, 1; MATHEMATICA With[{m=4}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *) PROG (PARI) T(n, k) = 6^(k*(n-k)); for (n=0, 11, for (k=0, n, print1(T(n, k), ", ")); print(); ); \\ Joerg Arndt, Feb 21 2014 (Magma) [6^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021 (Sage) flatten([[6^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021 CROSSREFS Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), this sequence (m=4), A176642 (m=6), A158117 (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26). Cf. this sequence (q=2), A176639 (q=3), A176641 (q=4). Sequence in context: A156601 A178232 A203338 * A172343 A058875 A156764 Adjacent sequences: A158113 A158114 A158115 * A158117 A158118 A158119 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Mar 12 2009 EXTENSIONS Overall edit and new name by Tom Edgar and Joerg Arndt, Feb 21 2014 STATUS approved

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Last modified September 27 05:14 EDT 2023. Contains 365674 sequences. (Running on oeis4.)