OFFSET
0,3
FORMULA
E.g.f.: exp(exp(x) - 1 - x^8/8!).
a(n) = n! * Sum_{k=0..floor(n/8)} (-1)^k * Bell(n-8*k) / ((n-8*k)! * k! * (8!)^k).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=8, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Apr 25 2021
MATHEMATICA
nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^8/8!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 8 k]/((n - 8 k)! k! (8!)^k), {k, 0, Floor[n/8]}], {n, 0, 25}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 8, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2021
STATUS
approved