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

0,3

Links

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

Formula

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

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

Example

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

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 *)

Crossrefs

Cf. A000009, A285229.

Sequence in context: A320793 A320794 A320795 * A089098 A129384 A131887

Adjacent sequences: A285227 A285228 A285229 * A285231 A285232 A285233

Keyword

nonn

Author

Alois P. Heinz, Apr 14 2017

Status

approved