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Search: id:A109084
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| A109084 |
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G.f. A(x) satisfies: A(x) = 1/G000041(x/A(x)) where G000041(x) is the g.f. of the partition numbers A000041. |
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2
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| 1, -1, -2, -5, -17, -63, -253, -1062, -4615, -20570, -93538, -432211, -2023567, -9578815, -45767162, -220431025, -1069079067, -5216655257, -25592441875, -126157044454, -624560659184, -3103962569509, -15480272621533, -77450458331100, -388627340240958, -1955249529839424
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Note: coefficient [x^n] A(x)^n = -A000203(n) (sum of divisors of n) for n>0.
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FORMULA
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G.f.: A(x) = x/series_reversion(x*eta(x)). G.f.: A(x) = 1/G109085(x) where G109085(x) is g.f. of A109085.
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EXAMPLE
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The initial terms [x^0] through [x^n] of n-th self-convolution
are persistently small:
A^0: 1;
A^1: 1,-1;
A^2: 1,-2,-3;
A^3: 1,-3,-3,-4;
A^4: 1,-4,-2,0,-7;
A^5: 1,-5,0,5,0,-6;
A^6: 1,-6,3,10,3,6,-12;
A^7: 1,-7,7,14,0,7,0,-8;
A^8: 1,-8,12,16,-10,0,-8,8,-15;
A^9: 1,-9,18,15,-27,-9,-21,0,0,-13;
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PROGRAM
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(PARI) a(n)=polcoeff(x/serreverse(x*eta(x+x*O(x^n))), n)
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CROSSREFS
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Cf. A109085, A000041, A000203.
Sequence in context: A084528 A112832 A003456 this_sequence A090902 A123166 A052539
Adjacent sequences: A109081 A109082 A109083 this_sequence A109085 A109086 A109087
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 18 2005
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