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Search: id:A073315
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| A073315 |
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Expansion of Lambert W function in powers of log(log(x))/log(x). |
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+0
1
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| 1, 1, 2, 2, 9, 6, 6, 44, 72, 24, 24, 250, 700, 600, 120, 120, 1644, 6750, 10200, 5400, 720, 720, 12348, 68208, 154350, 147000, 52920, 5040, 5040, 104544, 735392, 2274384, 3292800, 2163840, 564480, 40320, 40320, 986256, 8504928, 33911136
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth, On the Lambert W Function, Advances in Computational Mathematics, vol. 5, pp. 329-359, 1996.
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LINKS
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R. M. Corless et al., On the Lambert W Function.
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FORMULA
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E.g.f.: LambertW(x) = Sum_{n>0, k>=0} T(n, k)(-1/log(log(x)))^k(log(log(x))/log(x))^n/n!.
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EXAMPLE
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1; 1,2; 2,9,6; 6,44,72,24; 24,250,700,600,120; ...
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PROGRAM
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(PARI) T(n, k)=local(z, y); if(k<0|k>=n, 0, z=O(x); y='y; for(i=1, n+1, z=-log(1-x-x*y*z)); n!*polcoeff(polcoeff(z, n, x), k, y))
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CROSSREFS
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Sequence in context: A021002 A103710 A093589 this_sequence A066320 A005168 A011149
Adjacent sequences: A073312 A073313 A073314 this_sequence A073316 A073317 A073318
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KEYWORD
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nonn,tabl
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AUTHOR
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Michael Somos, Jul 24, 2002
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