OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..581
FORMULA
E.g.f.: exp(exp(x) - 1 - x^4/4!).
a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * Bell(n-4*k) / ((n-4*k)! * k! * (4!)^k).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=4, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
end:
seq(a(n), n=0..26); # Alois P. Heinz, Apr 25 2021
MATHEMATICA
nmax = 26; CoefficientList[Series[Exp[Exp[x] - 1 - x^4/4!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 4 k]/((n - 4 k)! k! (4!)^k), {k, 0, Floor[n/4]}], {n, 0, 26}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n - 1, k - 1] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 26}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2021
STATUS
approved