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Search: id:A005447
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| A005447 |
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Numerators of expansion of -W_{-1}(-e^{-1-x^2/2}) where W_{-1} is Lambert W function.
(Formerly M5399)
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+0
2
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| 1, 1, 1, 1, -1, 1, 1, -139, 1, -571, -281, 163879, -5221, 5246819, 5459, -534703531, 91207079, -4483131259, -2650986803, 432261921612371, -6171801683, 6232523202521089, 4283933145517, -25834629665134204969, 11963983648109
(list; graph; listen)
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OFFSET
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0,8
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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)); numerator(A[n])) /* Michael Somos Jun 09 2004 */
(PARI) a(n)=if(n<1, n==0, numerator(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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Sequence in context: A168531 A163693 A089518 this_sequence A169599 A047652 A020357
Adjacent sequences: A005444 A005445 A005446 this_sequence A005448 A005449 A005450
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KEYWORD
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sign,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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