OFFSET
0,3
COMMENTS
Also sum of the rightmost parts in all compositions of n into distinct parts.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000
FORMULA
EXAMPLE
a(6) = 30 = 1 + 1 + 2 + 2 + 3 + 3 + 2 + 4 + 1 + 5 + 6: (1)23, (1)32, (2)13, (2)31, (3)12, (3)21, (2)4, (4)2, (1)5, (5)1, (6).
MAPLE
b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, p!, b(n, i-1, p)+b(n-i, min(n-i, i-1), p+1)))
end:
a:= n-> `if`(n=0, 0, n*b(n$2, -1)):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[i*(i + 1)/2 < n, 0,
If[n == 0, p!, b[n, i - 1, p] + b[n - i, Min[n - i, i - 1], p + 1]]];
a[n_] := If[n == 0, 0, n*b[n, n, -1]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 13 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 07 2020
STATUS
approved