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A156691
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General qp weighted combinations as : m=2;q=3: 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, -5, 1, 1, 40, 40, 1, 1, -440, 3520, -440, 1, 1, 6160, 542080, 542080, 6160, 1, 1, -104720, 129015040, -1419165440, 129015040, -104720, 1, 1, 2094400, 43865113600, 6755227494400, 6755227494400, 43865113600, 2094400, 1, 1
(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, -3, 82, 2642, 1096482, -1161344798, 13598189404802, 633950903882665602,
301999235305843794118402, -782325471530406028574334585598,...},
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FORMULA
| m=2;q=3:
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, -5, 1},
{1, 40, 40, 1},
{1, -440, 3520, -440, 1},
{1, 6160, 542080, 542080, 6160, 1},
{1, -104720, 129015040, -1419165440, 129015040, -104720, 1},
{1, 2094400, 43865113600, 6755227494400, 6755227494400, 43865113600, 2094400, 1},
{1, -48171200, 20177952256000, -52825879006208000, 739562306086912000, -52825879006208000, 20177952256000, -48171200, 1},
{1, 1252451200, 12066415449088000, 631797512914247680000, 150367808073590947840000, 150367808073590947840000, 631797512914247680000, 12066415449088000, 1252451200, 1},
{1, -36321084800, 9098077248612352000, -10956632468958883266560000, 52153570552244284348825600000, -886610699388152833930035200000, 52153570552244284348825600000, -10956632468958883266560000, 9098077248612352000, -36321084800, 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: A058720 A015116 A174790 * A111820 A174912 A106238
Adjacent sequences: A156688 A156689 A156690 * A156692 A156693 A156694
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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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