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A176094
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A symmetrical triangle sequence:t(n,m)=Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];t1(n,m)=t(n,m)-t(n,0)+1
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0
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1, 1, 1, 1, 0, 1, 1, -78, -78, 1, 1, 1070, 1200, 1070, 1, 1, -16530, -14665, -14665, -16530, 1, 1, 240667, 179242, 163044, 179242, 240667, 1, 1, -2572332, -726012, -638358, -638358, -726012, -2572332, 1, 1, -29453058, -82571646, -81432978
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OFFSET
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0,8
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COMMENTS
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Row sums are:
{1, 2, 2, -154, 3342, -62388, 1002864, -7873402, -466190602, 41337748316,
-2470134563444,...}.
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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t(n,m)=Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];
;t1(n,m)=t(n,m)-t(n,0)+1
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EXAMPLE
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{1},
{1, 1},
{1, 0, 1},
{1, -78, -78, 1},
{1, 1070, 1200, 1070, 1},
{1, -16530, -14665, -14665, -16530, 1},
{1, 240667, 179242, 163044, 179242, 240667, 1},
{1, -2572332, -726012, -638358, -638358, -726012, -2572332, 1},
{1, -29453058, -82571646, -81432978, -79275240, -81432978, -82571646, -29453058, 1},
{1, 4090911030, 5625623025, 5495184255, 5457155847, 5457155847, 5495184255, 5625623025, 4090911030, 1},
{1, -244272466537, -288270741792, -281432018582, -280618259207, -280947591210, -280618259207, -281432018582, -288270741792, -244272466537, 1}
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MATHEMATICA
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t[n_, m_] = Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A117330 A033398 A204376 * A124289 A181467 A217006
Adjacent sequences: A176091 A176092 A176093 * A176095 A176096 A176097
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula, Apr 08 2010
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STATUS
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approved
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