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Search: id:A155869
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| A155869 |
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A sequence of polynomial coefficients related to a new form binomial: p(x,n)=If[n == 0, 1, (x + x^(n - 1) + Sum[Binomial[m*(n - m), n]*x^m, {m, 0, n}])/x]. |
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+0
1
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| 2, 1, 1, 1, 1, 1, 1, 6, 6, 1, 1, 28, 84, 28, 1, 1, 120, 792, 792, 120, 1, 1, 495, 6435, 12870, 6435, 495, 1, 1, 2002, 48620, 167960, 167960, 48620, 2002, 1, 1, 8008, 352716, 1961256, 3268760, 1961256, 352716, 8008, 1, 1, 31824, 2496144, 21474180
(list; table; graph; listen)
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OFFSET
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2,1
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COMMENT
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Row sums are:
{2, 2, 3, 14, 142, 1826, 26732, 437166, 7912722, 157258898, 3407186642,...}
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FORMULA
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p(x,n)=If[n == 0, 1, (x + x^(n - 1) + Sum[Binomial[m*(n - m), n]*x^m, {m, 0, n}])/x]
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{2},
{1, 1},
{1, 1, 1},
{1, 6, 6, 1},
{1, 28, 84, 28, 1},
{1, 120, 792, 792, 120, 1},
{1, 495, 6435, 12870, 6435, 495, 1},
{1, 2002, 48620, 167960, 167960, 48620, 2002, 1},
{1, 8008, 352716, 1961256, 3268760, 1961256, 352716, 8008, 1},
{1, 31824, 2496144, 21474180, 54627300, 54627300, 21474180, 2496144, 31824, 1},
{1, 125970, 17383860, 225792840, 834451800, 1251677700, 834451800, 225792840, 17383860, 125970, 1}
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MATHEMATICA
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Clear[p, n, m, x, a];
p[x_, n_] = If[n == 0, 1, (x + x^(n - 1) + Sum[Binomial[m*(n - m), n]*x^ m, {m, 0, n}])/x];
Table[ExpandAll[p[x, n]], {n, 2, 12}];
a = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 2, 12}];
Flatten[a]
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CROSSREFS
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Sequence in context: A082907 A146532 A119335 this_sequence A154338 A087436 A053255
Adjacent sequences: A155866 A155867 A155868 this_sequence A155870 A155871 A155872
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 29 2009
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