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A005146
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Numerators of numbers occurring in continued fraction connected with expansion of gamma function.
(Formerly M5308)
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4
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1, 1, 53, 195, 22999, 29944523, 109535241009, 29404527905795295658, 455377030420113432210116914702, 26370812569397719001931992945645578779849, 152537496709054809881638897472985990866753853122697839, 100043420063777451042472529806266909090824649341814868347109676190691
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. S. Wall, Analytic Theory of Continued Fractions, Chelsea 1973, p. 365.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..30
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
B. W. Char, On Stieltjes' continued fraction for the gamma function, Math. Comp., 34 (1980), 547-551.
Peter Luschny, Maple program for A005146/A005147
Peter Luschny, Continued fraction
W. Wang, Unified approaches to the approximations of the gamma function, J. Number Theory (2016).
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MATHEMATICA
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len = 12; s[p_] := (-1)^p * BernoulliB[2p+2]/(2p+1)/(2p+2); Do[m[n, 1] = 0, {n, 0, len}]; Do[m[n, 2] = s[n+1]/s[n], {n, 0, len-1}]; Do[m[n, k] =
If[OddQ[k], m[n+1, k-2]+m[n+1, k-1]-m[n, k-1],
m[n+1, k-2]*m[n+1, k-1]/m[n, k-1]], {k, 3, len}, {n, 0,
len-k+1}]; Do[m[n, 1] = s[n], {n, 0, len}];
Table[m[0, k], {k, 1, len}] // Numerator
(* Jean-François Alcover, May 24 2011, after Peter Luschny *)
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CROSSREFS
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Cf. A005147.
Sequence in context: A061664 A008993 A142088 * A158644 A158656 A013536
Adjacent sequences: A005143 A005144 A005145 * A005147 A005148 A005149
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KEYWORD
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nonn,frac,nice
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AUTHOR
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Simon Plouffe and N. J. A. Sloane
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EXTENSIONS
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More terms from Rainer Rosenthal, Jan 11 2007
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STATUS
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approved
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