A176641 Triangle T(n, k) = 28^(k*(n-k)), read by rows.

1, 1, 1, 1, 28, 1, 1, 784, 784, 1, 1, 21952, 614656, 21952, 1, 1, 614656, 481890304, 481890304, 614656, 1, 1, 17210368, 377801998336, 10578455953408, 377801998336, 17210368, 1, 1, 481890304, 296196766695424, 232218265089212416, 232218265089212416, 296196766695424, 481890304, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k, q) = c(n,q)/(c(k, q)*c(n-k, q)) where c(n, k) = Product_{j=1..n} (q*(2*q - 1))^j and q = 4.

From G. C. Greubel, Jun 30 2021: (Start)

T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 4.

T(n, k, m) = (m+2)^(k*(n-k)) with m = 26.

T(n, k, p) = binomial(p+2, 2)^(k*(n-k)) with p = 6. (End)

Example

Triangle begins as:
  1;
  1,        1;
  1,       28,            1;
  1,      784,          784,              1;
  1,    21952,       614656,          21952,            1;
  1,   614656,    481890304,      481890304,       614656,        1;
  1, 17210368, 377801998336, 10578455953408, 377801998336, 17210368, 1;

Mathematica

T[n_, k_, q_] = Binomial[2*q, 2]^(k*(n-k));
Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)
With[{m=26}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)

Prog

(Magma) [(28)^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[(28)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021

Crossrefs

Cf. A000384.

Cf. A158116 (q=2), A176639 (q=3), this sequence (q=4).

Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), A176642 (m=6), A158117 (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), this sequence (m=26).

Cf. A007318 (p=0), A118180 (p=1), A158116 (p=2), A158117 (p=3), A176639 (p=4), A176643 (p=5), this sequence (p=6).

Sequence in context: A347174 A352031 A174188 * A040796 A040797 A187595

Adjacent sequences: A176638 A176639 A176640 * A176642 A176643 A176644

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 22 2010

Extensions

Edited by G. C. Greubel, Jun 30 2021

Status

approved