A174923 T(n, m) = (n+m+1)!*m!/(n+1)! + (2*n-m+1)!*(n-m)!/(n+1)! - (2*n+1)!/(n+1).

1, 1, 1, 1, -32, 1, 1, -1195, -1195, 1, 1, -70554, -72408, -70554, 1, 1, -6531833, -6649664, -6649664, -6531833, 1, 1, -878169592, -889384176, -889565760, -889384176, -878169592, 1, 1, -161902540791, -163440763020, -163459004940, -163459004940, -163440763020, -161902540791, 1

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Formula

T(n, m) = (n+m+1)!*m!/(n+1)! + (2*n-m+1)!*(n-m)!/(n+1)! - (2*n+1)!/(n+1).

Example

Triangle begins:
  {1},
  {1, 1},
  {1, -32, 1},
  {1, -1195, -1195, 1},
  {1, -70554, -72408, -70554, 1},
  {1, -6531833, -6649664, -6649664, -6531833, 1},
  {1, -878169592, -889384176, -889565760, -889384176, -878169592, 1},
  {1, -161902540791, -163440763020, -163459004940, -163459004940, -163440763020, -161902540791, 1},
  ...

Mathematica

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

Crossrefs

Sequence in context: A086820 A354946 A351000 * A369651 A351809 A176341

Adjacent sequences: A174920 A174921 A174922 * A174924 A174925 A174926

Keyword

sign,tabl,less,easy

Author

Roger L. Bagula, Apr 02 2010

Status

approved