A176392 Triangle read by rows: T(n,k) = 2 - (1 + k)^k + (1 + n)^n - (1 - k + n)^(n - k).

1, 1, 1, 1, 7, 1, 1, 55, 55, 1, 1, 561, 609, 561, 1, 1, 7151, 7705, 7705, 7151, 1, 1, 109873, 117017, 117523, 117017, 109873, 1, 1, 1979503, 2089369, 2096465, 2096465, 2089369, 1979503, 1, 1, 40949569, 42929065, 43038883, 43045473, 43038883, 42929065, 40949569, 1

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

T(n,k) = T(n,n-k).

Example

Triangle begins:
  1;
  1,      1;
  1,      7,      1;
  1,     55,     55,      1;
  1,    561,    609,    561,      1;
  1,   7151,   7705,   7705,   7151,      1;
  1, 109873, 117017, 117523, 117017, 109873, 1;
  ...

Mathematica

t[n_, m_] = 2 - (1 + m)^m + (1 + n)^n - (1 - m + n)^(n - m);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Prog

(PARI) T(n, k) = 2 - (1 + k)^k + (1 + n)^n - (1 - k + n)^(n - k) \\ Andrew Howroyd, Nov 19 2025

Crossrefs

Sequence in context: A174689 A172345 A174719 * A015118 A340428 A174691

Adjacent sequences: A176389 A176390 A176391 * A176393 A176394 A176395

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 16 2010

Status

approved