A172177 Triangle T(n, k) = 1 + abs(n! - k!)*abs(n! - (n-k)!), read by rows.

1, 1, 1, 1, 2, 1, 1, 21, 21, 1, 1, 415, 485, 415, 1, 1, 11425, 13453, 13453, 11425, 1, 1, 431401, 499729, 509797, 499729, 431401, 1, 1, 21768481, 24786961, 25250545, 25250545, 24786961, 21768481, 1, 1, 1422454321, 1596592801, 1620622801, 1623767617, 1620622801, 1596592801, 1422454321, 1

Offset

0,5

Links

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

Formula

T(n, k) = 1 + abs(n! - k!)*abs(n! - (n-k)!).

Example

Triangle begins as:
  1;
  1,        1;
  1,        2,        1;
  1,       21,       21,        1;
  1,      415,      485,      415,        1;
  1,    11425,    13453,    13453,    11425,        1;
  1,   431401,   499729,   509797,   499729,   431401,        1;
  1, 21768481, 24786961, 25250545, 25250545, 24786961, 21768481, 1;

Mathematica

T[n_, k_]= 1 +Abs[n!-k!]*Abs[n!-(n-k)!];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma)
F:=Factorial; [1 + Abs(F(n)-F(k))*Abs(F(n)-F(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 29 2021
(Sage)
f=factorial; flatten([[1 + abs(f(n)-f(k))*abs(f(n)-f(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 29 2021

Crossrefs

Sequence in context: A157453 A174174 A156889 * A156725 A141904 A246072

Adjacent sequences: A172174 A172175 A172176 * A172178 A172179 A172180

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Jan 28 2010

Extensions

Edited by G. C. Greubel, Apr 29 2021

Status

approved