OFFSET
0,3
FORMULA
E.g.f.: 1 / (2 + x^4/4! - exp(x)).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=4, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
MATHEMATICA
nmax = 21; CoefficientList[Series[1/(2 + x^4/4! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 29 2021
STATUS
approved