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).

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

Stanislav Sykora, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A231530 A231531 A231532 * A231534 A231535 A231536

Keyword

nonn,cons

Author

Stanislav Sykora, Nov 10 2013

Status

approved