A158116 Triangle T(n,k) = 6^(k*(n-k)), read by rows.

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

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