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URL: https://oeis.org/A174923

⇱ A174923 - OEIS

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A174923
T(n, m) = (n+m+1)!*m!/(n+1)! + (2*n-m+1)!*(n-m)!/(n+1)! - (2*n+1)!/(n+1).
0
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
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
KEYWORD
sign,tabl,less,easy
AUTHOR
Roger L. Bagula, Apr 02 2010
STATUS
approved