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Search: id:A075264
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| A075264 |
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Triangle of numerators of coefficients, where the n-th row forms the polynomial in z, P(n,z), that is the coefficient of x^n in {-ln(1-x)/x}^z, for n>0. The denominator for all the terms in the n-th row is A053657(n). |
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5
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| 1, 5, 3, 6, 5, 1, 502, 485, 150, 15, 760, 802, 305, 50, 3, 152696, 171150, 73801, 15435, 1575, 63, 252336, 295748, 139020, 33817, 4515, 315, 9, 51360816, 62333204, 31231500, 8437975, 1334760, 124110, 6300, 135, 88864128, 110941776, 58415444
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Each n-th row polynomial, P(n,z), has a trivial zero at z=0; for odd rows, P(2n+1,z) also has zeros at z=-2n, z=-(2n+1), for n>0.
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FORMULA
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The n-th row polynomials, P(n, z), satisfy 1 + sum_{n>=1} P(n, z) x^n = {sum_{k>=1} x^(k-1)/k }^z.
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EXAMPLE
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P(1,z)=z/2,
P(2,z)=(5z + 3z^2)/24,
P(3,z)=(6z + 5z^2 + z^3)/48,
P(4,z)=(502z + 485z^2 + 150z^3 + 15z^4)/5760,
P(5,z)=(760z + 802z^2 + 305z^3 + 50z^4 +3z^5)/11520,
P(6,z)=(152696z + 171150z^2 + 73801z^3 + 15435z^4 + 1575z^5
+ 63z^6)/2903040,
P(7,z)=(252336z + 295748z^2 + 139020z^3 + 33817z^4 + 4515z^5
+ 315z^6 + 9z^7)/5806080,
P(8,z)=(51360816z + 62333204z^2 + 31231500z^3 + 8437975z^4
+ 1334760z^5 + 124110z^6 + 6300z^7 + 135z^8)/1393459200.
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x^2*O(x^n)); D=1; for(j=0, n, D=lcm(D, denominator( polcoeff(polcoeff((-log(1-X)/x)^z+z*O(z^j), j, z), n, x)))); return(D*polcoeff(polcoeff((-log(1-X)/x)^z+z*O(z^k), k, z), n, x))}
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CROSSREFS
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Cf. A053657.
Adjacent sequences: A075261 A075262 A075263 this_sequence A075265 A075266 A075267
Sequence in context: A021655 A072424 A089250 this_sequence A011504 A097907 A066253
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KEYWORD
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frac,nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 15 2002; revised Jun 27 2005
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