cp's OEIS Frontend

A344680 Number of partitions of n that are also multiplicity multiset of a partition of 2n.

%I A344680 #17 Aug 17 2021 06:17:04
%S A344680 1,1,2,3,4,4,8,8,12,14,18,21,30,33,41,49,62,70,86,98,116,133,160,181,
%T A344680 214,237,282,311,364,407,466,522,600,652,761,815,937,1038,1179,1271,
%U A344680 1442,1577,1762,1930,2158,2311,2636,2831,3146,3402,3784,4057,4537,4869,5365,5745,6370,6802,7562,8061,8785,9471,10410
%N A344680 Number of partitions of n that are also multiplicity multiset of a partition of 2n.
%F A344680 a(n) = A337584(2n,n).
%e A344680 a(0) = 1: [].
%e A344680 a(1) = 1: [1].
%e A344680 a(2) = 2: [2], [1,1].
%e A344680 a(3) = 3: [3], [1,2], [1,1,1].
%e A344680 a(4) = 4: [4], [1,3], [2,2], [1,1,2].
%e A344680 a(5) = 4: [5], [1,4], [1,1,3], [1,2,2].
%e A344680 a(6) = 8: [6], [1,5], [2,4], [3,3], [1,1,4], [1,2,3], [2,2,2], [1,1,1,3].
%e A344680 a(7) = 8: [7], [1,6], [1,1,5], [1,2,4], [1,3,3], [2,2,3], [1,1,1,4], [1,1,2,3].
%p A344680 b:= proc(n, i) option remember; `if`(n=0 or i=1, `if`(n=0, {[]}, {[n]}),
%p A344680      {b(n, i-1)[], seq(map(x-> sort([x[], j]), b(n-i*j, i-1))[], j=1..n/i)})
%p A344680     end:
%p A344680 a:= n-> nops(select(l-> add(i, i=l)=n, b(2*n$2))):
%p A344680 seq(a(n), n=0..30);
%Y A344680 Cf. A088887, A337584.
%K A344680 nonn
%O A344680 0,3
%A A344680 _Alois P. Heinz_, Aug 17 2021