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A005147 Denominators of numbers occurring in continued fraction connected with expansion of gamma function.

%I A005147 M4831 #32 May 08 2018 15:11:54
%S A005147 12,30,210,371,22737,19733142,48264275462,9769214287853155785,
%T A005147 113084128923675014537885725485,
%U A005147 5271244267917980801966553649147604697542,24274291553105128438297398108902195365373879212227726,13346384670164266280033479022693768890138348905413621178450736182873
%N A005147 Denominators of numbers occurring in continued fraction connected with expansion of gamma function.
%D A005147 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
%D A005147 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005147 Vincenzo Librandi, <a href="/A005147/b005147.txt">Table of n, a(n) for n = 0..30</a>
%H A005147 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A005147 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 258.
%H A005147 B. W. Char, <a href="http://www.jstor.org/stable/2006103">On Stieltjes' continued fraction for the gamma function</a>, Math. Comp., 34 (1980), 547-551.
%H A005147 Peter Luschny, <a href="/A005146/a005146.txt">Maple program for A005146/A005147</a>
%H A005147 Peter Luschny, <a href="http://www.luschny.de/math/factorial/approx/continuedfraction.html">Continued fraction</a>
%H A005147 W. Wang, <a href="http://dx.doi.org/10.1016/j.jnt.2015.12.016">Unified approaches to the approximations of the gamma function</a>, J. Number Theory (2016).
%t A005147 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] =
%t A005147 If[OddQ[k], m[n+1, k-2]+m[n+1, k-1]-m[n, k-1],
%t A005147 m[n+1, k-2]*m[n+1, k-1]/m[n, k-1]], {k, 3, len}, {n, 0,
%t A005147 len-k+1}]; Do[m[n, 1] = s[n], {n, 0, len}];
%t A005147 Table[m[0, k], {k, 1, len}] // Denominator
%t A005147 (* _Jean-François Alcover_, May 24 2011, after _Peter Luschny_ *)
%Y A005147 Cf. A005146.
%K A005147 nonn,frac,nice
%O A005147 0,1
%A A005147 _Simon Plouffe_ and _N. J. A. Sloane_
%E A005147 More terms from _Rainer Rosenthal_, Jan 11 2007