A176644 Triangle T(n, k) = 40^(k*(n-k)), read by rows.

1, 1, 1, 1, 40, 1, 1, 1600, 1600, 1, 1, 64000, 2560000, 64000, 1, 1, 2560000, 4096000000, 4096000000, 2560000, 1, 1, 102400000, 6553600000000, 262144000000000, 6553600000000, 102400000, 1, 1, 4096000000, 10485760000000000, 16777216000000000000, 16777216000000000000, 10485760000000000, 4096000000, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..40 of the triangle, flattened

Formula

T(n, k, q) = c(n,q)/(c(k, q)*c(n-k, q)) where c(n, q) = (q*(3*q - 2))^binomial(n+1,2) and q = 4.

T(n, k, q) = (q*(3*q-2))^(k*(n-k)) with q = 4.

T(n, k, m) = (m+2)^(k*(n-k)) with m = 38. - G. C. Greubel, Jul 01 2021

Example

Triangle begins as:
  1;
  1,         1;
  1,        40,             1;
  1,      1600,          1600,               1;
  1,     64000,       2560000,           64000,             1;
  1,   2560000,    4096000000,      4096000000,       2560000,         1;
  1, 102400000, 6553600000000, 262144000000000, 6553600000000, 102400000, 1;

Mathematica

T[n_, k_, q_]:= (q*(3*q-2))^(k*(n-k)); Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten
Table[(40)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 01 2021 *)

Prog

(Magma) [40^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 01 2021
(Sage) flatten([[40^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 01 2021

Crossrefs

Cf. A000567.

Cf. A176642 (q=2), A176643 (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), A176641 (m=26), this sequence (m=38).

Sequence in context: A013419 A013420 A156917 * A329337 A078084 A037937

Adjacent sequences: A176641 A176642 A176643 * A176645 A176646 A176647

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 22 2010

Extensions

Edited by G. C. Greubel, Jul 01 2021

Status

approved