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A005146
Numerators of numbers occurring in continued fraction connected with expansion of gamma function.
(Formerly M5308)
4
1, 1, 53, 195, 22999, 29944523, 109535241009, 29404527905795295658, 455377030420113432210116914702, 26370812569397719001931992945645578779849, 152537496709054809881638897472985990866753853122697839, 100043420063777451042472529806266909090824649341814868347109676190691
OFFSET
0,3
REFERENCES
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.
LINKS
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, Continued fraction
MATHEMATICA
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 *)
CROSSREFS
Cf. A005147.
Sequence in context: A008993 A142088 A330810 * A158644 A158656 A013536
KEYWORD
nonn,frac,nice
EXTENSIONS
More terms from Rainer Rosenthal, Jan 11 2007
STATUS
approved