A173476 Triangle T(n, k) = 1 + (k!)^2 - 2*k!*(n-k)! + ((n-k)!)^2, read by rows.

1, 1, 1, 2, 1, 2, 26, 2, 2, 26, 530, 26, 1, 26, 530, 14162, 530, 17, 17, 530, 14162, 516962, 14162, 485, 1, 485, 14162, 516962, 25391522, 516962, 13925, 325, 325, 13925, 516962, 25391522, 1625621762, 25391522, 515525, 12997, 1, 12997, 515525, 25391522, 1625621762

Offset

0,4

Links

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Formula

T(n, k) = 1 + ( (n-k)! - k! )^2.

Sum_{k=0..n} T(n, k) = 1 + n + 2*A061062(n) - 2*A003149(n). - G. C. Greubel, Feb 19 2021

Example

Triangle begins as:
           1;
           1,        1;
           2,        1,      2;
          26,        2,      2,    26;
         530,       26,      1,    26, 530;
       14162,      530,     17,    17, 530, 14162;
      516962,    14162,    485,     1, 485, 14162, 516962;
    25391522,   516962,  13925,   325, 325, 13925, 516962, 25391522;
  1625621762, 25391522, 515525, 12997,   1, 12997, 515525, 25391522, 1625621762;

Mathematica

Table[((n-k)! -k!)^2 +1, {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 19 2021 *)

Prog

(Sage) flatten([[(factorial(n-k) -factorial(k))^2 +1 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 19 2021
(Magma) [(Factorial(n-k) -Factorial(k))^2 +1: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 19 2021

Crossrefs

Cf. A003149, A061062.

Sequence in context: A051502 A228690 A121721 * A281129 A136156 A191657

Adjacent sequences: A173473 A173474 A173475 * A173477 A173478 A173479

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 19 2010

Extensions

Edited by G. C. Greubel, Feb 19 2021

Status

approved