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Search: id:A096797
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| A096797 |
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Triangle of coefficients, read by row polynomials P_n(y), that satisfy the g.f.: A038497(x,y) = Product_{n>=1} 1/(1-x^n)^[P_n(y)/n], with P_n(0)=0 for n>=1 and P_0(0)=1. |
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+0
2
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| 1, 3, 1, 8, 0, 1, 16, -1, 0, 1, 34, -15, 0, 0, 1, 54, -40, 3, 0, 0, 1, 104, -119, 21, 0, 0, 0, 1, 156, -260, 88, -1, 0, 0, 0, 1, 261, -576, 305, -27, 0, 0, 0, 0, 1, 382, -1111, 850, -155, 3, 0, 0, 0, 0, 1, 615, -2167, 2167, -638, 33, 0, 0, 0, 0, 0, 1, 842, -3854, 5056, -2164, 240, -1, 0, 0, 0, 0, 0, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A038497 is the matrix square of partition triangle A008284. The first column forms the Moebius transform of {n*A000041(n), n>=1}. The inverse Moebius transform of each column forms the columns of triangle {n/k*A096798(n,k)}.
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EXAMPLE
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1/A038497(x,y) =
(1-x)^y*(1-x^2)^[(3y+y^2)/2]*(1-x^3)^[(8y+y^3)/3]*(1-x^4)^[(16y-y^2+y^4)/
4]*(1-x^5)^[(34y-15y^2+y^5)/5]*...
Rows begin:
[1],
[3,1],
[8,0,1],
[16,-1,0,1],
[34,-15,0,0,1],
[54,-40,3,0,0,1],
[104,-119,21,0,0,0,1],
[156,-260,88,-1,0,0,0,1],
[261,-576,305,-27,0,0,0,0,1],
[382,-1111,850,-155,3,0,0,0,0,1],
[615,-2167,2167,-638,33,0,0,0,0,0,1],
[842,-3854,5056,-2164,240,-1,0,0,0,0,0,1],
[1312,-6916,11089,-6409,1183,-39,0,0,0,0,0,0,1],
[1782,-11649,23037,-17241,4704,-343,3,0,0,0,0,0,0,1],...
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CROSSREFS
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Cf. A038497, A008284, A096798.
Adjacent sequences: A096794 A096795 A096796 this_sequence A096798 A096799 A096800
Sequence in context: A096643 A036575 A060487 this_sequence A084246 A141252 A059526
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 13 2004
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