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A266692
Number of partitions of n with product of multiplicities of parts equal to 9.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 3, 2, 4, 5, 7, 7, 14, 13, 18, 25, 29, 35, 47, 54, 65, 86, 101, 120, 147, 174, 205, 254, 291, 347, 419, 486, 565, 676, 779, 908, 1065, 1228, 1425, 1668, 1906, 2198, 2547, 2912, 3336, 3841, 4384, 4998, 5728, 6513, 7404, 8436
OFFSET
0,10
LINKS
FORMULA
a(n) ~ c * exp(Pi*sqrt(n/3)) * n^(1/4), where c = 0.004308121528... - Vaclav Kotesovec, May 24 2018
EXAMPLE
a(9) = 2: [1,1,1,1,1,1,1,1,1], [1,1,1,2,2,2].
a(11) = 1: [1,1,1,1,1,1,1,1,1,2].
a(12) = 3: [1,1,1,1,1,1,1,1,1,3], [1,1,1,2,2,2,3], [1,1,1,3,3,3].
MAPLE
b:= proc(n, i, p) option remember; `if`(i*(p+(i-1)/2)<n, 0, `if`(n=0,
`if`(p=1, 1, 0), b(n, i-1, p) +add(`if`(irem(p, j)>0, 0, (h->
b(h, min(h, i-1), p/j))(n-i*j)), j=1..min(p, n/i))))
end:
a:= b(n$2, 9):
seq(a(n), n=0..65);
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[i*(p + (i - 1)/2) < n, 0, If[n == 0, If[p == 1, 1, 0], b[n, i - 1, p] + Sum[If[Mod[p, j] > 0, 0, Function[h, b[h, Min[h, i - 1], p/j]][n - i*j]], {j, 1, Min[p, n/i]}]]];
a[n_] := b[n, n, 9];
Table[a[n], {n, 0, 65}] (* Jean-François Alcover, May 01 2018, translated from Maple *)
CROSSREFS
Column k=9 of A266477.
Sequence in context: A147785 A067591 A097609 * A077884 A331103 A267724
KEYWORD
nonn
AUTHOR
STATUS
approved