OFFSET
0,5
COMMENTS
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..440
FORMULA
From Peter Luschny, Oct 23 2015: (Start)
a(n) = Re(i!*(n-i)!)*sinh(Pi)/Pi.
a(n) = n!*[x^n](cos(log(1-x))/(1-x)).
a(n) = Sum_{k=0..floor(n/2)} (-1)^(n+k)*Stirling1(n+1,2*k+1).
a(n) = Re(rf(1+i,n)) where rf(k,n) is the rising factorial and i the imaginary unit.
a(n) = (-1)^n*A009454(n+1). (End)
EXAMPLE
factim(5,1) = -90 + 190*i. Hence a(5) = -90.
MAPLE
seq(simplify(Re(I!*(n-I)!)*sinh(Pi)/Pi), n=0..22); # Peter Luschny, Oct 23 2015
MATHEMATICA
Table[Re[Product[k+I, {k, n}]], {n, 0, 30}] (* Harvey P. Dale, Aug 04 2016 *)
PROG
(PARI) Factim(nmax, m)={local(a, k); a=vector(nmax); a[1]=1+0*I;
for (k=2, nmax, a[k]=a[k-1]*(k-1+m*I); ); return(a); }
a = Factim(1000, 1); real(a)
(Sage)
A231530 = lambda n : rising_factorial(1-I, n).real()
[A231530(n) for n in range(24)] # Peter Luschny, Oct 23 2015
(Python)
from sympy.functions.combinatorial.numbers import stirling
def A231530(n): return sum(stirling(n+1, (k<<1)+1, kind=1)*(-1 if k&1 else 1) for k in range((n>>1)+1)) # Chai Wah Wu, Feb 22 2024
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Stanislav Sykora, Nov 10 2013
STATUS
approved