OFFSET
2,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..2213
MAPLE
h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
`if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
a:= n-> (k-> A(n, k)-A(n, k-1))(2):
seq(a(n), n=2..32);
MATHEMATICA
h[n_, m_, t_, k_] := h[n, m, t, k] = If[m == 0, Binomial[n + t, t],
If[n == 0, 0, Sum[h[n - 1, m - j, t + 1, k], {j, 1, Min[k, m]}]]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
Sum[b[n - i*j, i - 1, k]*h[A[i, k], j, 0, k], {j, 0, n/i}]]];
A[n_, k_] := If[n < 2, n, b[n - 1, n - 1, k]];
a[n_] := A[n, 2] - A[n, 1];
Table[a[n], {n, 2, 32}] (* Jean-François Alcover, Dec 01 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 04 2018
STATUS
approved