OFFSET
4,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 4..1000
FORMULA
a(n) ~ 3^(n-1) / (3! * QPochhammer[1/3]). - Vaclav Kotesovec, Oct 25 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(4):
seq(a(n), n=4..40);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, k^(n - 1), b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]];
A[n_, k_] := If[n == 0, 1, If[k < 2, k, k b[n, n, k - 1]]];
a[n_] := With[{k = 4}, Sum[A[n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}]];
a /@ Range[4, 40] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2018
STATUS
approved