OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 - 3*x*A(x) - x * A(x/(1 - x)) / (1 - x).
a(n) = exp(1) * Sum_{k>=0} (-1)^k * (k-3)^n / k!.
a(0) = 1; a(n) = -3*a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
a(n) = Sum_{k=0..n} binomial(n,k) * (-3)^(n-k) * A000587(k).
MATHEMATICA
nmax = 27; CoefficientList[Series[Exp[1 - 3 x - Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -3 a[n - 1] - Sum[Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 27}]
Table[Sum[Binomial[n, k] (-3)^(n - k) BellB[k, -1], {k, 0, n}], {n, 0, 27}]
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(1 - 3*x - exp(x)))) \\ Michel Marcus, Dec 02 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 01 2023
STATUS
approved