OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..386
FORMULA
a(n) = n! * [x^n] exp(n*x)*sin(x). - Ilya Gutkovskiy, Apr 10 2018
a(n) ~ sin(1) * n^n. - Vaclav Kotesovec, Jun 08 2019
a(n) = Sum_{j=0..floor((n-1)/2)} binomial(n,2*j+1)*n^(n-2*j-1)*(-1)^j. - Chai Wah Wu, Feb 15 2024
a(n) = -(i/2)*((n + i)^n - (n - i)^n) where i is the imaginary unit. - Gerry Martens, Dec 30 2024
MAPLE
seq(Im((n+I)^n), n=0..20); # Robert Israel, Dec 30 2024
MATHEMATICA
Table[Im[(n + I)^n], {n, 0, 17}] (* Robert G. Wilson v, Jan 23 2006 *)
PROG
(PARI) a(n) = imag((n + I)^n); \\ Michel Marcus, Apr 11 2018
(Python)
from math import comb
def A115416(n): return sum(comb(n, j)*n**(n-j)*(-1 if j-1&2 else 1) for j in range(1, n+1, 2)) # Chai Wah Wu, Feb 15 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Reinhard Zumkeller, Jan 22 2006
EXTENSIONS
More terms from Robert G. Wilson v, Jan 23 2006
STATUS
approved