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Search: id:A078521
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| A078521 |
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Signed triangle of D'Arcais numbers (A008298) : coefficients of r in the polynomials generated by the series coefficients of z^n in Product[(1-z^k)^r, {k,1,Inf}]*(n!). |
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+0
1
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| 1, 0, -1, 0, -3, 1, 0, -8, 9, -1, 0, -42, 59, -18, 1, 0, -144, 450, -215, 30, -1, 0, -1440, 3394, -2475, 565, -45, 1, 0, -5760, 30912, -28294, 9345, -1225, 63, -1, 0, -75600, 293292, -340116, 147889, -27720, 2338, -84, 1, 0, -524160, 3032208, -4335596, 2341332, -579369, 69552, -4074, 108, -1, 0, -6531840
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OFFSET
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1,5
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COMMENT
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Row sums give A010815 * n!.
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FORMULA
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See Mathematica line
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EXAMPLE
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The z-expansion of Product[(1-z^k)^r, {k,1,3}] is 1 - r*z + ((-3+r)*r*z^2)/2 -(r*(8-9*r +r^2)*z^3)/6, so the third row of the triangle is 0,-8,9,-1
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MATHEMATICA
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w=16; (CoefficientList[ #, r]&/@ CoefficientList[Series[Product[(1-z^k)^r, {k, 1, w}], {z, 0, w}], z])Range[0, w]!
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CROSSREFS
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Cf. A010815, A008298.
Sequence in context: A052420 A103685 A162971 this_sequence A137432 A135871 A126178
Adjacent sequences: A078518 A078519 A078520 this_sequence A078522 A078523 A078524
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KEYWORD
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easy,sign
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 07 2003
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