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A176641 Triangle T(n, k) = 28^(k*(n-k)), read by rows. 9
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 (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, 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: A347162 A347174 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

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Last modified October 18 18:47 EDT 2021. Contains 348068 sequences. (Running on oeis4.)