A282132 - OEIS

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A282132

Imaginary part of n!*Sum_{k=1..n} i^(k-1)/k, where i is sqrt(-1).

0, 1, 3, 6, 30, 300, 2100, 11760, 105840, 1421280, 15634080, 147692160, 1919998080, 33106993920, 496604908800, 6638004172800, 112846070937600, 2386916704972800, 45351417394483200, 785383247480832000, 16493048197097472000, 413938002507853824000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Daniel Suteu, Table of n, a(n) for n = 1..100

FORMULA

a(n) ~ log(sqrt(2)) * n!.

a(1) = 0, a(n+1) = a(n)*(n+1) + n!*sin(Pi*n/2).

EXAMPLE

For n=5, a(5) = 30, which is the imaginary part of 5!*(1/1 + i/2 - 1/3 - i/4 + 1/5) = 104+30*i.

PROG

(PARI) a(n) = imag(n!*sum(k=1, n, I^(k-1)/k));