A174923 A symmetrical triangle sequence: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

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

Offset

0,5

Comments

The name contains an unmatched parenthesis. - Editors, Mar 13 2024

Row sums are:

{1, 2, -30, -2388, -213514, -26362992, -4424673294, -977604617500,

-276059341118418, -97172808944838504, -41757197999307047062,...}.

Links

Table of n, a(n) for n=0..31.

Formula

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

Example

{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},
{1, -39230231039990, -39518230751780, -39520796507280, -39520824520320, -39520796507280, -39518230751780, -39230231039990, 1},
{1, -12093372555263989, -12164016030566136, -12164505889525704, -12164509997063424, -12164509997063424, -12164505889525704, -12164016030566136, -12093372555263989, 1},
{1, -4622513815535615988, -4644508232680242888, -4644630298138508496, -4644631100102535360, -4644631106393241600, -4644631100102535360, -4644630298138508496, -4644508232680242888, -4622513815535615988, 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,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved