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 A231534 Decimal expansion of the absolute value of Sum_{n=0..inf}(1/c_n), c_0=1, c_n=c_(n-1)*(n+I). 3
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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. LINKS Stanislav Sykora, Table of n, a(n) for n = 1..10000 FORMULA abs(Sum_{n=0..inf}(1/(A231530(n)+A231531(n)*I))). EXAMPLE 1.8426202983147305389585438... 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); } abs(Expim(1, 1)) CROSSREFS Cf. A231532 (real part), A231533 (imaginary part), and A231530, A231531 (respectively, the real and imaginary parts of the expansion coefficient's denominators) Sequence in context: A222301 A198353 A010523 * A014391 A099286 A089729 Adjacent sequences:  A231531 A231532 A231533 * A231535 A231536 A231537 KEYWORD nonn,cons AUTHOR Stanislav Sykora, Nov 10 2013 STATUS approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)