A115416 Imaginary part of (n + i)^n, with i=sqrt(-1).

0, 1, 4, 26, 240, 2876, 42372, 740536, 14970816, 343603216, 8825080100, 250756091552, 7809130867824, 264489160965056, 9678967816041188, 380574552503498624, 16000787866533953280, 716309568462681538816

Offset

0,3

Comments

Real part: A115415.

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

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

Cf. A000312, A009116, A115415.

Sequence in context: A209923 A317339 A304338 * A302606 A052577 A203935

Adjacent sequences: A115413 A115414 A115415 * A115417 A115418 A115419

Keyword

nonn

Author

Reinhard Zumkeller, Jan 22 2006

Extensions

More terms from Robert G. Wilson v, Jan 23 2006

Status

approved