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A115416
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Imaginary part of (n + i)^n, with i=sqrt(-1).
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8
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0, 1, 4, 26, 240, 2876, 42372, 740536, 14970816, 343603216, 8825080100, 250756091552, 7809130867824, 264489160965056, 9678967816041188, 380574552503498624, 16000787866533953280, 716309568462681538816
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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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
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MATHEMATICA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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