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A231533
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).
3
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, 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, 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
OFFSET
0,1
COMMENTS
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.
LINKS
FORMULA
imag(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))).
EXAMPLE
-0.92856077732184558666720293...
PROG
(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); }
imag(Expim(1, 1))
CROSSREFS
Cf. A231532, A231534, and A231530, A231531 (respectively the real and imaginary parts of the expansion coefficient's denominators).
Sequence in context: A252001 A098784 A105172 * A011453 A125580 A086238
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Nov 10 2013
STATUS
approved