A174923 - OEIS

%I #5 Mar 13 2024 19:20:32

%S 1,1,1,1,-32,1,1,-1195,-1195,1,1,-70554,-72408,-70554,1,1,-6531833,

%T -6649664,-6649664,-6531833,1,1,-878169592,-889384176,-889565760,

%U -889384176,-878169592,1,1,-161902540791,-163440763020,-163459004940

%N 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

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

%C Row sums are:

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

%C -276059341118418, -97172808944838504, -41757197999307047062,...}.

%F 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

%e {1},

%e {1, 1},

%e {1, -32, 1},

%e {1, -1195, -1195, 1},

%e {1, -70554, -72408, -70554, 1},

%e {1, -6531833, -6649664, -6649664, -6531833, 1},

%e {1, -878169592, -889384176, -889565760, -889384176, -878169592, 1},

%e {1, -161902540791, -163440763020, -163459004940, -163459004940, -163440763020, -161902540791, 1},

%e {1, -39230231039990, -39518230751780, -39520796507280, -39520824520320, -39520796507280, -39518230751780, -39230231039990, 1},

%e {1, -12093372555263989, -12164016030566136, -12164505889525704, -12164509997063424, -12164509997063424, -12164505889525704, -12164016030566136, -12093372555263989, 1},

%e {1, -4622513815535615988, -4644508232680242888, -4644630298138508496, -4644631100102535360, -4644631106393241600, -4644631100102535360, -4644630298138508496, -4644508232680242888, -4622513815535615988, 1}

%t 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;

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 02 2010