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A088880
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Number of different values of A000005(m) when A056239(m) is equal to n.
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11
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1, 1, 2, 2, 5, 4, 8, 6, 12, 10, 16, 13, 25, 18, 28, 25, 40, 32, 51, 40, 62, 51, 76, 62, 99, 77, 112, 92, 138, 109, 165, 130, 189, 153, 220, 178, 267, 208, 292, 240, 347, 274, 397, 315, 445, 361, 512, 407, 591, 464, 647, 524, 746, 588, 830, 664, 928, 746, 1034
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OFFSET
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0,3
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COMMENTS
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Number of distinct values of Product_{k=1..n} (m(k,P)+1) where m(k,P) is multiplicity of part k in partition P, as P ranges over all partitions of n. - Vladeta Jovovic, May 24 2008
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LINKS
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MAPLE
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multipl := proc(P, p)
local a;
a := 0 ;
for el in P do
if el = p then
a := a+1 ;
end if;
end do;
a ;
end proc:
local pro, pa, m, p;
pro := {} ;
for pa in combinat[partition](n) do
m := 1 ;
for p from 1 to n do
m := m*(1+multipl(pa, p)) ;
end do:
pro := pro union {m} ;
end do:
nops(pro) ;
# second Maple program
b:= proc(n, i) option remember; `if`(n=0 or i<2, {n+1},
{seq(map(p->p*(j+1), b(n-i*j, i-1))[], j=0..n/i)})
end:
a:= n-> nops(b(n, n)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n==0 || i<2, {n+1}, Table[b[n-i*j, i-1]*(j+1), {j, 0, n/i}] // Flatten // Union]; a[n_] := Length[b[n, n]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jan 08 2016, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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