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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
OFFSET
0,5
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
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