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A176639 Triangle T(n, k) = 15^(k*(n-k)), read by rows. 14
1, 1, 1, 1, 15, 1, 1, 225, 225, 1, 1, 3375, 50625, 3375, 1, 1, 50625, 11390625, 11390625, 50625, 1, 1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1, 1, 11390625, 576650390625, 129746337890625, 129746337890625, 576650390625, 11390625, 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 = 3.

T(n, k, q) = binomial(2*q, 2)^(k*(n-k)) with q = 3.

T(n, k, m) = (m+2)^(k*(n-k)) with m = 13. - G. C. Greubel, Jun 30 2021

EXAMPLE

Triangle begins as:

  1;

  1,      1;

  1,     15,          1;

  1,    225,        225,           1;

  1,   3375,      50625,        3375,          1;

  1,  50625,   11390625,    11390625,      50625,      1;

  1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1;

MATHEMATICA

(* First program *)

T[n_, k_, q_] = Binomial[2*q, 2]^(k*(n-k));

Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)

(* Second program *)

With[{m=13}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)

PROG

(Magma) [(15)^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021

(Sage) flatten([[(15)^(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), this sequence (q=3), A176641 (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), this sequence (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26).

Sequence in context: A174693 A340430 A022178 * A015139 A040231 A040232

Adjacent sequences:  A176636 A176637 A176638 * A176640 A176641 A176642

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 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)