%I #8 Jan 07 2016 10:26:08
%S 4,6,6,2,0,1,6,7,0,3,1,8,2,1,1,1,3,4,0,9,1,1,0,7,0,3,6,4,1,2,4,0,8,6,
%T 8,5,1,3,5,5,9,8,1,8,6,2,0,1,7,7,8,3,7,0,2,9,1,1,4,2,1,3,0,6,2,8,9,4,
%U 6,2,2,5,7,1,1,2,1,4,7,1,2,0,6,0,4,1,2,0,7,5,5,0,5,5,7,1,9,4,7,2,9,9,0,8,2
%N Decimal expansion of area bounded by x->x and x->Log[x! ] on 0 <= x <= c, where c is the value given by A078335.
%e 4.66201670318211134091107036412...
%t RealDigits[NIntegrate[x - Log[x! ], {x, 0, FindRoot[r - Log[r! ], {r,5.29}, WorkingPrecision -> 200][[1]][[2]]}, WorkingPrecision -> 40]]
%o (PARI) intnum(x=0, solve(x=5.2, 5.3, exp(x)-gamma(1+x)) , x - log(gamma(x+1))) \\ _Michel Marcus_, Apr 05 2015
%Y Cf. Upper bound of integral is given by A078335.
%K cons,nonn
%O 1,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 30 2006
%E More terms from _Robert G. Wilson v_, Jan 07 2016