OFFSET
0,3
COMMENTS
The ratio a(n)/A121626(n) converges to c for odd n and to -1/c for even n for n -> oo with c = 0.6420926... (= cot(1) (A073449) from Moritz Firsching, Feb 14 2024). See linked plots.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..350
Hugo Pfoertner, Plot of ratio a(n)/A121626(n), using Plot 2.
Hugo Pfoertner, Plot of asinh(a(n)) vs asinh(A121626(n)), using Plot 2.
FORMULA
a(n) = Sum_{j=0..floor((n-1)/2)} binomial(n,2*j+1)*n^(2*j+1)*(-1)^j. - Chai Wah Wu, Feb 15 2024
MATHEMATICA
Array[Im[(1+#*I)^#] &, 25, 0] (* Paolo Xausa, Feb 19 2024 *)
PROG
(PARI) a370189(n) = imag((1+I*n)^n)
(Python)
from math import comb
def A370189(n): return sum(comb(n, j)*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
sign,easy
AUTHOR
Hugo Pfoertner, Feb 14 2024
STATUS
approved