OFFSET
0,2
FORMULA
a(n) = exp(1) * Sum_{k>=0} (-1)^k * (3*k-1)^n / k!.
a(0) = 1; a(n) = -a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k).
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * A000587(k).
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[1 - x - Exp[3 x]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[Binomial[n - 1, k - 1] 3^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
Table[Sum[(-1)^(n - k) Binomial[n, k] 3^k BellB[k, -1], {k, 0, n}], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 29 2023
STATUS
approved