OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
For n = 3 the 12 overcompositions of 3 are [3], [3'], [1, 2], [1', 2], [1, 2'], [1', 2'], [2, 1], [2', 1], [2, 1'], [2', 1'], [1, 1, 1], [1', 1, 1]. There are 24 parts, so a(3) = 24.
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
`if`(i<1, 0, add((p-> p+[0, p[1]*j])(1/j!*
`if`(j>0, 2, 1)*b(n-i*j, i-1, p+j)), j=0..n/i)))
end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..35); # Alois P. Heinz, Apr 28 2016
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0}, If[i < 1, {0, 0}, Sum[# + {0, #[[1]]*j}&[1/j!*If[j > 0, 2, 1]*b[n - i*j, i - 1, p + j]], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 03 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 01 2014
EXTENSIONS
a(6)-a(30) from Alois P. Heinz, Feb 02 2014
STATUS
approved