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A055535
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Denominators in expansion of (1-x)^(-1/x)/e.
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2
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1, 2, 24, 16, 5760, 2304, 580608, 165888, 1393459200, 309657600, 73574645760, 13377208320, 24103053950976000, 3708162146304000, 578473294823424000, 77129772643123200, 9440684171518279680000, 100969884187361280000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Or, equally, denominators in expansion of (1+x)^(1/x)/e.
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 293, Problem 11.
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3.1.
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FORMULA
| Comments from Miklos Kristof (kristmikl(AT)freemail.hu), Nov 04 2007 (Start): (1+x)^(1/x) = exp(log(1+x)/x) = exp(1)*exp(-x/2)*exp(x^2/3)*exp(x^3/4)*...
Let a(n) be A055505, let b(n) be this sequence. Then (1+x)^(1/x) = exp(1)*a(n)/b(n) x^n.
a(n)/b(n) = sum(s(i,i-n)/(i !), i = n,...,infinity),... where s(n,m) is a Stirling number of the first kind.
exp(1) = 1+sum(s(i,i)/i !,i = 1,... infinity), for the n = 1 case.
a(1)/b(1) = 1/1 because 1+1/1!+1/2!+1/3!+1/4!+... = exp(1)
a(2)/b(2) = 1/2 because 1/2!+3/3!+6/4!+10/5!+... = 1/2*exp(1)
a(3)/b(3) = 11/24 because 2/3!+11/4!+35/5!+85/6!+... = 11/24*exp(1)
a(4)/b(4) = 7/16 because 6/4!+50/5!+225/6!+735/7!+... = 7/16*exp(1) (End)
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EXAMPLE
| (1-x)^(-1/x) = exp(1)*(1 + 1/2*x + 11/24*x^2 + 7/16*x^3 + 2447/5760*x^4 + 959/2304*x^5 + 238043/580608*x^6 + ...).
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CROSSREFS
| Cf. A094638, A130534, A055505.
Sequence in context: A066585 A075267 A002743 * A072217 A052686 A064818
Adjacent sequences: A055532 A055533 A055534 * A055536 A055537 A055538
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 11 2000
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 25 2008 at the suggestion of R. J. Mathar and Eric S. Rowland.
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