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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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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: A045045 A108156 A089518 this_sequence A047652 A020357 A050967
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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njas
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EXTENSIONS
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Edited by Michael Somos, Jul 21, 2002
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