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A174945
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)
0
1, 1, 1, 1, -21, 1, 1, -1173, -1173, 1, 1, -70521, -72353, -70521, 1, 1, -6531789, -6649565, -6649565, -6531789, 1, 1, -878169537, -889384022, -889565551, -889384022, -878169537, 1, 1, -161902540725, -163440762800, -163459004566
OFFSET
0,5
COMMENTS
Row sums are:
{1, 2, -19, -2344, -213393, -26362706, -4424672667, -977604616180,
-276059341115701, -97172808944832982, -41757197999307035919,...}
FORMULA
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);
out_n,m,q=t(n,m,q)-t(n,0,q)+1
EXAMPLE
{1},
{1, 1},
{1, -21, 1},
{1, -1173, -1173, 1},
{1, -70521, -72353, -70521, 1},
{1, -6531789, -6649565, -6649565, -6531789, 1},
{1, -878169537, -889384022, -889565551, -889384022, -878169537, 1},
{1, -161902540725, -163440762800, -163459004566, -163459004566, -163440762800, -161902540725, 1},
{1, -39230231039913, -39518230751483, -39520796506675, -39520824519561, -39520796506675, -39518230751483, -39230231039913, 1},
{1, -12093372555263901, -12164016030565751, -12164505889524791, -12164509997062049, -12164509997062049, -12164505889524791, -12164016030565751, -12093372555263901, 1},
{1, -4622513815535615889, -4644508232680242404, -4644630298138507187, -4644631100102533061, -4644631106393238839, -4644631100102533061, -4644630298138507187, -4644508232680242404, -4622513815535615889, 1}
MATHEMATICA
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);
Table[Flatten[Table[Table[t[ n, m, q] - t[n, 0, q] + 1, {m, 0, n}], {n, 0, 10}]], {q, 0, 1, 1/12}]
CROSSREFS
Sequence in context: A022184 A176643 A015147 * A040450 A040451 A040449
KEYWORD
sign,tabl,uned
AUTHOR
Roger L. Bagula, Apr 02 2010
STATUS
approved