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A344680
Number of partitions of n that are also multiplicity multiset of a partition of 2n.
1
1, 1, 2, 3, 4, 4, 8, 8, 12, 14, 18, 21, 30, 33, 41, 49, 62, 70, 86, 98, 116, 133, 160, 181, 214, 237, 282, 311, 364, 407, 466, 522, 600, 652, 761, 815, 937, 1038, 1179, 1271, 1442, 1577, 1762, 1930, 2158, 2311, 2636, 2831, 3146, 3402, 3784, 4057, 4537, 4869, 5365, 5745, 6370, 6802, 7562, 8061, 8785, 9471, 10410
OFFSET
0,3
FORMULA
a(n) = A337584(2n,n).
EXAMPLE
a(0) = 1: [].
a(1) = 1: [1].
a(2) = 2: [2], [1,1].
a(3) = 3: [3], [1,2], [1,1,1].
a(4) = 4: [4], [1,3], [2,2], [1,1,2].
a(5) = 4: [5], [1,4], [1,1,3], [1,2,2].
a(6) = 8: [6], [1,5], [2,4], [3,3], [1,1,4], [1,2,3], [2,2,2], [1,1,1,3].
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].
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, `if`(n=0, {[]}, {[n]}),
{b(n, i-1)[], seq(map(x-> sort([x[], j]), b(n-i*j, i-1))[], j=1..n/i)})
end:
a:= n-> nops(select(l-> add(i, i=l)=n, b(2*n$2))):
seq(a(n), n=0..30);
CROSSREFS
Sequence in context: A319079 A325329 A224038 * A330147 A241037 A097093
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 17 2021
STATUS
approved