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A156690
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General qp weighted combinations as : m=1;q=2: t(n,m)=If[m == 0, n!, Product[Product[1 - (i + 1)*(m + 1), {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]
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3
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1, 1, 1, 1, -3, 1, 1, 15, 15, 1, 1, -105, 525, -105, 1, 1, 945, 33075, 33075, 945, 1, 1, -10395, 3274425, -22920975, 3274425, -10395, 1, 1, 135135, 468242775, 29499294825, 29499294825, 468242775, 135135, 1, 1, -2027025, 91307341125
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, -1, 32, 317, 68042, -16392913, 59935345472, 443114522425577, 41952026212764267602,
-11773681484663891313796273,...},
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FORMULA
| m=1;q=2:
t(n,m)=If[m == 0, n!, Product[Product[1 - (i + 1)*(m + 1), {i, 0, k - 1}], {k, 1, n}]];
b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]
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EXAMPLE
| {1},
{1, 1},
{1, -3, 1},
{1, 15, 15, 1},
{1, -105, 525, -105, 1},
{1, 945, 33075, 33075, 945, 1},
{1, -10395, 3274425, -22920975, 3274425, -10395, 1},
{1, 135135, 468242775, 29499294825, 29499294825, 468242775, 135135, 1},
{1, -2027025, 91307341125, -63275987399625, 569483886596625, -63275987399625, 91307341125, -2027025, 1},
{1, 34459425, 23283371986875, 209759898229756875, 20766229924745930625, 20766229924745930625, 209759898229756875, 23283371986875, 34459425, 1},
{1, -654729075, 7520529151760625, -1016286706923172059375, 1307960991810122440415625, -14387570909911346844571875, 1307960991810122440415625, -1016286706923172059375, 7520529151760625, -654729075, 1}
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MATHEMATICA
| t[n_, m_] = If[m == 0, n!, Product[Product[1 - (i + 1)*(m + 1), {i, 0, k - 1}], {k, 1, n}]];
b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];
Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]
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CROSSREFS
| Sequence in context: A176225 A173917 A174410 * A176248 A060325 A135021
Adjacent sequences: A156687 A156688 A156689 * A156691 A156692 A156693
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 13 2009
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