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A370554
a(n) is the denominator of the imaginary part of Product_{k=1..n} (1 + i/k) where i is the imaginary unit.
6
1, 2, 3, 3, 12, 24, 252, 56, 18144, 5184, 199584, 33264, 2395008, 48384, 50295168, 100590336, 804722688, 146313216, 137607579648, 6552741888, 11559036690432, 1216740704256, 2924436282679296, 835553223622656, 70186470784303104, 226043384168448, 1895034711176183808
OFFSET
1,2
FORMULA
a(n) = denominator of A231531(n)/n!. - Chai Wah Wu, Feb 22 2024
EXAMPLE
See A370551.
PROG
(PARI) a370554(n) = denominator(imag(prod(k=1, n, 1+I/k)))
(Python)
from math import factorial, gcd
from sympy.functions.combinatorial.numbers import stirling
def A370554(n): return (a:=factorial(n))//gcd(a, sum(stirling(n+1, k<<1, kind=1)*(1 if k&1 else -1) for k in range((n+1>>1)+1))) # Chai Wah Wu, Feb 22 2024
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Hugo Pfoertner, Feb 22 2024
STATUS
approved