A285230 Number of multisets of exactly n partitions of positive integers into distinct parts with total sum of parts equal to 2n.

1, 1, 3, 5, 11, 19, 37, 63, 115, 195, 339, 566, 957, 1573, 2599, 4217, 6842, 10962, 17531, 27767, 43862, 68769, 107469, 166942, 258461, 398124, 611237, 934356, 1423724, 2161145, 3270560, 4932647, 7418099, 11121610, 16629101, 24794130, 36874451, 54698714

Offset: 0

Author

Alois P. Heinz, Apr 14 2017

Keywords

• nonn

Examples

			a(3) = 5: {4,1,1}, {31,1,1}, {3,2,1}, {21,2,1}, {2,2,2}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A285229.

Programs

Maple

with(numtheory):
g:= proc(n) option remember; `if`(n=0, 1, add(add(
     `if`(d::odd, d, 0), d=divisors(j))*g(n-j), j=1..n)/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*g(d+1), d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..50);

Mathematica

g[n_] := g[n] = If[n == 0, 1, Sum[Sum[If[OddQ[d], d, 0], {d, Divisors[j]}]* g[n - j], {j, 1, n}]/n];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*g[d + 1], {d, Divisors[j]}]*a[n - j], {j, 1, n}]/n];
a /@ Range[0, 50] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^A000009(j+1).

a(n) = A285229(2n,n).