OFFSET
3,1
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 3..5000 (terms 3..2000 from Alois P. Heinz)
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
`if`(k=0, [1, 1], `if`(i<2, 0, b(n, i-1, k))+
(h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*
b(n-i, min(n-i, i), k)))(b(i$2, k-1))))
end:
a:= n-> (k-> add(b(n$2, i)[2]*(-1)^(k-i)*binomial(k, i), i=0..k))(2):
seq(a(n), n=3..35);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 0, b[n, i - 1, k]] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/ h[[1]]}][h[[1]] b[n - i, Min[n - i, i], k]]][b[i, i, k - 1]]]];
a[n_] := With[{k = 2}, Sum[b[n, n, i][[2]] (-1)^(k-i) Binomial[k, i], {i, 0, k}]];
a /@ Range[3, 35] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 02 2019
STATUS
approved