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%I #21 Nov 05 2023 14:15:19
%S 2,2,6,6,5,3,4,5,0,7,6,9,9,8,4,8,8,3,5,0,7,1,9,6,3,8,5,7,6,7,8,2,2,0,
%T 9,1,8,4,0,8,8,2,9,7,1,4,2,8,0,2,2,2,1,9,3,8,6,1,0,9,3,5,5,4,4,2,9,1,
%U 8,8,9,9,7,6,9,1,3,7,5,2,8,1,0,8,5,0,9,1,0,6,9,7,4,7,9,3,4,0,6,9,5,8,8,4
%N Decimal expansion of Integral_{0..oo} 1/Gamma(1+x) dx, a variation of the Fransén-Robinson constant.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 263.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Fransen-RobinsonConstant.html">Fransén-Robinson Constant</a>
%F Also equals e - Integral_{-oo..oo} e^(-e^x)/(x^2 + Pi^2) dx (observed by Ramanujan).
%e 2.266534507699848835071963857678220918408829714280222193861...
%t NIntegrate[1/Gamma[1 + x], {x, 0, Infinity}, WorkingPrecision -> 104] // RealDigits // First
%o (Python)
%o from mpmath import *
%o mp.dps = 200
%o A247377 = [d for d in nstr(quad(lambda x:1/gamma(1+x),[0,inf]),n=mp.dps)[:-1] if d != '.'] # _Chai Wah Wu_, Sep 16 2014
%o (PARI)
%o localprec(100); intnum(x=0,[[1], 1],1/gamma(1+x)) \\ _Dumitru Damian_, Oct 12 2023
%Y Cf. A058655.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Sep 15 2014
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