OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..4000
EXAMPLE
a(3) = 8 = 1+2+2+3 counting the parts in 3, 21, 2|1, 1|1|1.
MAPLE
g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [1, 0], g(n, i-1)+ (f-> f+
[0, f[1]])(g(n-i, min(n-i, i-1)))))
end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0],
`if`(i<2, 0, b(n, i-1)) +(h-> (f-> f +[0, f[1]*
h[2]/h[1]])(b(n-i, min(n-i, i))*h[1]))(g(i$2)))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..37);
MATHEMATICA
g[n_, i_] := g[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, {1, 0}, g[n, i - 1] + Function[f, f + {0, f[[1]]}][g[n - i, Min[n - i, i - 1]]]]];
b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 2, 0, b[n, i - 1]] + Module[{h, f}, h = g[i, i]; f = b[n - i, Min[n - i, i]] h[[1]]; f + {0, f[[1]] h[[2]]/h[[1]]}]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 37] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 18 2019
STATUS
approved