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Search: id:A005446
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| A005446 |
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Denominators of expansion of -W_{-1}(-e^{-1-x^2/2}) where W_{-1} is Lambert W function.
(Formerly M3140)
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+0
2
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| 1, 1, 3, 36, 270, 4320, 17010, 5443200, 204120, 2351462400, 1515591000, 2172751257600, 354648294000, 10168475885568000, 7447614174000, 1830325659402240000, 1595278956070800000, 2987091476144455680000
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. M. Borwein and R. M. Corless, Emerging Tools for Experimental Mathematics, Amer. Math. Monthly, 106 (No. 10, 1999), 889-909.
G. Marsaglia and J. C. W. Marsaglia, A new derivation of Stirling's approximation to n!, Amer. Math. Monthly, 97 (1990), 827-829.
E. T. Copson, An Introduction to the Theory of Functions of a Complex Variable, 1935, Oxford University Press, p. 221.
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FORMULA
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G.f.: A(x)=Sum_{n>=0} A005447(n)/A005446(n)x^n satisfies log(A(x))=A(x)-1-x^2/2.
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PROGRAM
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(PARI) a(n)=local(A); if(n<1, n==0, A=vector(n, k, 1); for(k=2, n, A[k]=(A[k-1]-sum(i=2, k-1, i*A[i]*A[k+1-i]))/(k+1)); denominator(A[n])) /* Michael Somos Jun 09 2004 */
(PARI) a(n)=if(n<1, n==0, denominator(polcoeff(serreverse(sqrt(2*(x-log(1+x+x^2*O(x^n))))), n))) /* Michael Somos Jun 09 2004 */
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CROSSREFS
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Cf. A005447.
Sequence in context: A068619 A073992 A127960 this_sequence A056307 A056299 A073980
Adjacent sequences: A005443 A005444 A005445 this_sequence A005447 A005448 A005449
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Michael Somos, Jul 21, 2002
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