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A005147 Denominators of numbers occurring in continued fraction connected with expansion of gamma function.
(Formerly M4831)
4
12, 30, 210, 371, 22737, 19733142, 48264275462, 9769214287853155785, 113084128923675014537885725485, 5271244267917980801966553649147604697542, 24274291553105128438297398108902195365373879212227726, 13346384670164266280033479022693768890138348905413621178450736182873 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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}] // Denominator

(* Jean-Fran├žois Alcover, May 24 2011, after P. Luschny *)

CROSSREFS

Cf. A005146.

Sequence in context: A080563 A221520 A214311 * A007308 A065138 A279821

Adjacent sequences:  A005144 A005145 A005146 * A005148 A005149 A005150

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.