This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115416 #31 Jan 11 2025 19:12:56
%S A115416 0,1,4,26,240,2876,42372,740536,14970816,343603216,8825080100,
%T A115416 250756091552,7809130867824,264489160965056,9678967816041188,
%U A115416 380574552503498624,16000787866533953280,716309568462681538816
%N A115416 Imaginary part of (n + i)^n, with i=sqrt(-1).
%H A115416 Seiichi Manyama, <a href="/A115416/b115416.txt">Table of n, a(n) for n = 0..386</a>
%F A115416 a(n) = n! * [x^n] exp(n*x)*sin(x). - _Ilya Gutkovskiy_, Apr 10 2018
%F A115416 a(n) ~ sin(1) * n^n. - _Vaclav Kotesovec_, Jun 08 2019
%F A115416 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
%F A115416 a(n) = -(i/2)*((n + i)^n - (n - i)^n) where i is the imaginary unit. - _Gerry Martens_, Dec 30 2024
%p A115416 seq(Im((n+I)^n), n=0..20); # _Robert Israel_, Dec 30 2024
%t A115416 Table[Im[(n + I)^n], {n, 0, 17}] (* _Robert G. Wilson v_, Jan 23 2006 *)
%o A115416 (PARI) a(n) = imag((n + I)^n); \\ _Michel Marcus_, Apr 11 2018
%o A115416 (Python)
%o A115416 from math import comb
%o A115416 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
%Y A115416 Cf. A000312, A009116, A115415 (real part).
%K A115416 nonn
%O A115416 0,3
%A A115416 _Reinhard Zumkeller_, Jan 22 2006
%E A115416 More terms from _Robert G. Wilson v_, Jan 23 2006