A005147 Denominators of numbers occurring in continued fraction connected with expansion of gamma function. (Formerly M4831)

12, 30, 210, 371, 22737, 19733142, 48264275462, 9769214287853155785, 113084128923675014537885725485, 5271244267917980801966553649147604697542, 24274291553105128438297398108902195365373879212227726, 13346384670164266280033479022693768890138348905413621178450736182873

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.

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.

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).

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-François Alcover, May 24 2011, after Peter Luschny *)

Crossrefs

Cf. A005146.

Sequence in context: A080563 A221520 A214311 * A320122 A007308 A065138

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