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%I #14 Dec 11 2013 23:17:49
%S 1,8,4,2,6,2,0,2,9,8,3,1,4,7,3,0,5,3,8,9,5,8,5,4,3,8,6,6,6,9,0,8,7,1,
%T 4,3,3,0,5,5,2,0,3,2,7,8,2,6,4,7,4,9,1,9,6,8,4,2,8,6,0,3,2,0,5,4,7,0,
%U 6,5,1,1,5,1,0,3,0,2,0,1,7,3,1,4,9,3,8,7,2,6,7,8,3,3,0,4,8,1,6,1,2,8,0,5,6
%N Decimal expansion of the absolute value of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I).
%C Consider an extension of exp(x) to an intriguing function, expim(x,y), defined by the power series Sum_{n=0..inf}(x^n/c_n), where c_0 = 1, c_n = c_(n-1)*(n+y*I), so that exp(x) = expim(x,0). The current sequence regards the absolute value of expim(1,1). The decimal expansions of the real and imaginary parts of expim(1,1) are in A231532 and A231533, respectively.
%H Stanislav Sykora, <a href="/A231534/b231534.txt">Table of n, a(n) for n = 1..10000</a>
%F abs(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))).
%e 1.8426202983147305389585438...
%o (PARI) Expim(x, y)={local (c, k, lastval, val); c = 1.0+0.0*I; lastval = c; k = 1; while (k, c*=x/(k + y*I); val = lastval + c; if (val==lastval, break); lastval = val; k += 1; ); return (val); }
%o abs(Expim(1, 1))
%Y Cf. A231532 (real part), A231533 (imaginary part), and A231530, A231531 (respectively, the real and imaginary parts of the expansion coefficient's denominators)
%K nonn,cons
%O 1,2
%A _Stanislav Sykora_, Nov 10 2013
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