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).

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

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 * A348908 A014391 A099286

Adjacent sequences: A231531 A231532 A231533 * A231535 A231536 A231537

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 10 2013

Status

approved