OFFSET
0,2
FORMULA
O.g.f.: 1/(1 + 2*x/(1 - 2*x/(1 + 2*x/(1 - 4*x/(1 + 2*x/(1 - 6*x/(1 + 2*x/(1 - 8*x/(1 + ...))))))))), a continued fraction.
a(0) = 1; a(n) = -Sum_{k=1..n} 2^k*binomial(n-1,k-1)*a(n-k).
a(n) = exp(1) * 2^n * Sum_{k>=0} (-1)^k*k^n/k!.
a(n) = 2^n * A000587(n).
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[1 - Exp[2x]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = -Sum[2^k Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
Table[2^n BellB[n, -1], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 06 2019
STATUS
approved