OFFSET
0,3
COMMENTS
The first negative term is a(71).
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * Bell(n-2*k-1).
Conjecture: a(n) = (i/(2*e))*Sum_{k=0..oo} ((k - i)^n - (k + i)^n)/(k!), where i = sqrt(-1) and e = exp(1). - Velin Yanev, Jul 06 2024
MATHEMATICA
nmax = 25; CoefficientList[Series[Sin[x] Exp[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k Binomial[n, 2 k + 1] BellB[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}], {n, 0, 25}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 07 2022
STATUS
approved