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%I #13 Nov 12 2013 16:38:27
%S 9,2,8,5,6,0,7,7,7,3,2,1,8,4,5,5,8,6,6,6,7,2,0,2,9,3,2,8,5,6,6,9,8,7,
%T 2,0,2,8,9,8,6,9,7,4,6,3,3,1,5,6,5,6,5,9,9,9,2,3,1,4,8,3,3,9,0,9,9,5,
%U 0,0,6,1,7,0,2,6,0,3,6,5,9,7,6,7,1,9,0,7,4,5,8,4,5,5,1,2,2,7,1,8,1,0,0,7,1
%N Decimal expansion of the negative imaginary part 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 negative imaginary part of the complex expim(1,1). The decimal expansion of the real part is in A231532 and that of the absolute value in A231534.
%H Stanislav Sykora, <a href="/A231533/b231533.txt">Table of n, a(n) for n = 0..10000</a>
%F imag(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))).
%e -0.92856077732184558666720293...
%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 imag(Expim(1,1))
%Y Cf. A231532, A231534, and A231530, A231531 (respectively the real and imaginary parts of the expansion coefficient's denominators).
%K nonn,cons
%O 0,1
%A _Stanislav Sykora_, Nov 10 2013
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