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A067764
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Numerators of the coefficients in exp(x/(1-x)) power series.
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3
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1, 3, 13, 73, 167, 4051, 37633, 43817, 4596553, 58941091, 274691047, 12470162233, 202976401213, 1178339174801, 65573803186921, 99264170666917, 994319127823939, 588633468315403843, 13564373693588558173
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Define c(n)=A067764(n)/A067653(n). For a given sequence s(n) consider P[s(n)](z):=e^(-z/(1-z))*sum{k>=0, s(k)c(k)z^k}. Regarding complex valued abelian limitation the following holds true: if s(n) is convergent (to the limit s) then lim P[s(n)](z)=s as z tends to +1 in a certain sub-domain D of the unit circle. There are two constraints: (1) D contains the line [0,1[. (2) There is a d>0 such that the intersection of {w|Re(w)>1-d} and D is a non-empty subset of a generalized Stolz set defined by {w||Im(w)|<=t*(1-Re(w))^(3/2)}, t<1. If z tends to +1 from outside such a domain that limit doesn't exist in general. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 20 2010
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REFERENCES
| K. Knopp, Theory and Application of Infinite Series, Dover p. 547.
O. Perron, Uber das infinitare Verhalten der koeffizienten einer gewissen Potenzreihe, Archiv d. math. u. Phys. (3), Vol. 22, pp. 329-340, 1914.
D. Borwein, On methods of summability based on power series, Proc. royal Soc. Edinburgh, Sect. A 64 (1959).
H. Fischer, Eine Theorie komplexwertiger Abelscher Limitierungsmethoden (A theory of complex valued abelian limitation methods), Dissertation (1987), pp. 29-32.
K. Zeller, W. Beekmann, Theorie der Limitierungsverfahren, Springer-Verlag, Berlin (1970).
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FORMULA
| a(n) is the numerator of sum(i=1, n, C(n-1, i-1)/i!)
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CROSSREFS
| Cf. A067653.
Sequence in context: A047159 A086662 A090754 * A193930 A063512 A199317
Adjacent sequences: A067761 A067762 A067763 * A067765 A067766 A067767
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KEYWORD
| nonn,frac
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2002
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