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%I #22 Feb 15 2024 20:47:48
%S 0,1,4,26,240,2876,42372,740536,14970816,343603216,8825080100,
%T 250756091552,7809130867824,264489160965056,9678967816041188,
%U 380574552503498624,16000787866533953280,716309568462681538816
%N Imaginary part of (n + i)^n, with i=sqrt(-1).
%C Real part: A115415.
%H Seiichi Manyama, <a href="/A115416/b115416.txt">Table of n, a(n) for n = 0..386</a>
%F a(n) = n! * [x^n] exp(n*x)*sin(x). - _Ilya Gutkovskiy_, Apr 10 2018
%F a(n) ~ sin(1) * n^n. - _Vaclav Kotesovec_, Jun 08 2019
%F 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
%t Table[Im[(n + I)^n], {n, 0, 17}] (* _Robert G. Wilson v_, Jan 23 2006 *)
%o (PARI) a(n) = imag((n + I)^n); \\ _Michel Marcus_, Apr 11 2018
%o (Python)
%o from math import comb
%o 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 Cf. A000312, A009116, A115415.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, Jan 22 2006
%E More terms from _Robert G. Wilson v_, Jan 23 2006
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