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%I #21 Nov 04 2020 15:38:40
%S 0,1,3,15,114,1242,17129,284714,5526741,122592633,3057488913,
%T 84665033543,2576896828787,85495426794698,3070641026296061,
%U 118685141706060740,4911825483278949553,216697390123422589527,10151899714746097960699,503310218588181014061292
%N Nearest integer to Integral_{x=0..n} x^x dx.
%C The antiderivative of x^x cannot be described in terms of elementary functions.
%C a(1)=1 is the rounding of A083648.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SophomoresDream.html">Sophomore's Dream</a>
%e Integral_{X=0..4} x^x dx = 114.119062..., so a(4) = 114.
%e Integral_{x=0..7} x^x dx = 284713.7347218579997..., so a(7) = 284714.
%t Table[Round[NIntegrate[x^x,{x,0,n},WorkingPrecision->100]],{n,0,20}] (* _Harvey P. Dale_, Nov 04 2020 *)
%o (PARI) for(k=0,19,print1(round(intnum(x=0,k,x^x)),", ")) \\ _Hugo Pfoertner_, Jan 18 2020
%Y Cf. A000312, A083648.
%K nonn
%O 0,3
%A _Eliora Ben-Gurion_, Jan 10 2020
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