%I #2 Mar 30 2012 17:34:40
%S 1,1,1,1,-21,1,1,-1173,-1173,1,1,-70521,-72353,-70521,1,1,-6531789,
%T -6649565,-6649565,-6531789,1,1,-878169537,-889384022,-889565551,
%U -889384022,-878169537,1,1,-161902540725,-163440762800,-163459004566
%N A symmetrical triangle sequence based on:q=1/12;t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!* m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q)
%C Row sums are:
%C {1, 2, -19, -2344, -213393, -26362706, -4424672667, -977604616180,
%C -276059341115701, -97172808944832982, -41757197999307035919,...}
%F q=1/12;
%F t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!* m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q);
%F out_n,m,q=t(n,m,q)-t(n,0,q)+1
%e {1},
%e {1, 1},
%e {1, -21, 1},
%e {1, -1173, -1173, 1},
%e {1, -70521, -72353, -70521, 1},
%e {1, -6531789, -6649565, -6649565, -6531789, 1},
%e {1, -878169537, -889384022, -889565551, -889384022, -878169537, 1},
%e {1, -161902540725, -163440762800, -163459004566, -163459004566, -163440762800, -161902540725, 1},
%e {1, -39230231039913, -39518230751483, -39520796506675, -39520824519561, -39520796506675, -39518230751483, -39230231039913, 1},
%e {1, -12093372555263901, -12164016030565751, -12164505889524791, -12164509997062049, -12164509997062049, -12164505889524791, -12164016030565751, -12093372555263901, 1},
%e {1, -4622513815535615889, -4644508232680242404, -4644630298138507187, -4644631100102533061, -4644631106393238839, -4644631100102533061, -4644630298138507187, -4644508232680242404, -4622513815535615889, 1}
%t t[n_, m_, q_] = 12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!*m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q);
%t Table[Flatten[Table[Table[t[ n, m, q] - t[n, 0, q] + 1, {m, 0, n}], {n, 0, 10}]], {q, 0, 1, 1/12}]
%K sign,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Apr 02 2010