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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 (list; graph; refs; listen; history; text; internal format)
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.

B. W. Char, On Stieltjes' continued fraction for the gamma function, Math. Comp., 34 (1980), 547-551.

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

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.

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).

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-Fran├žois Alcover, May 24 2011, after Peter Luschny *)

CROSSREFS

Cf. A005147.

Sequence in context: A061664 A008993 A142088 * A158644 A158656 A013536

Adjacent sequences:  A005143 A005144 A005145 * A005147 A005148 A005149

KEYWORD

nonn,frac,nice

AUTHOR

Simon Plouffe and N. J. A. Sloane

EXTENSIONS

More terms from Rainer Rosenthal, Jan 11 2007

STATUS

approved

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Last modified September 20 16:14 EDT 2017. Contains 292276 sequences.