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A285230 Number of multisets of exactly n partitions of positive integers into distinct parts with total sum of parts equal to 2n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 5 16:17 EDT 2022. Contains 357259 sequences. (Running on oeis4.)