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A280275 Number of set partitions of [n] where sizes of distinct blocks are coprime. 3
1, 1, 2, 5, 12, 37, 118, 387, 1312, 4445, 17034, 73339, 342532, 1616721, 7299100, 31195418, 129179184, 578924785, 3057167242, 18723356715, 120613872016, 738703713245, 4080301444740, 20353638923275, 95273007634552, 443132388701107, 2149933834972928 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Wikipedia, Coprime integers
FORMULA
a(n) = Sum_{k=0..n} A280880(n,k).
EXAMPLE
a(n) = A000110(n) for n<=3.
a(4) = 12: 1234, 123|4, 124|3, 12|3|4, 134|2, 13|2|4, 1|234, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4.
a(5) = 37: 12345, 1234|5, 1235|4, 123|45, 123|4|5, 1245|3, 124|35, 124|3|5, 125|34, 12|345, 125|3|4, 12|3|4|5, 1345|2, 134|25, 134|2|5, 135|24, 13|245, 135|2|4, 13|2|4|5, 145|23, 14|235, 15|234, 1|2345, 1|234|5, 1|235|4, 1|23|4|5, 145|2|3, 14|2|3|5, 1|245|3, 1|24|3|5, 1|2|345, 1|2|34|5, 15|2|3|4, 1|25|3|4, 1|2|35|4, 1|2|3|45, 1|2|3|4|5.
MAPLE
with(numtheory):
b:= proc(n, i, s) option remember;
`if`(n=0 or i=1, 1, b(n, i-1, select(x->x<=i-1, s))+
`if`(i>n or factorset(i) intersect s<>{}, 0, b(n-i, i-1,
select(x->x<=i-1, s union factorset(i)))*binomial(n, i)))
end:
a:= n-> b(n$2, {}):
seq(a(n), n=0..30);
MATHEMATICA
b[n_, i_, s_] := b[n, i, s] = Expand[If[n==0 || i==1, x^n, b[n, i-1, Select[s, # <= i-1&]] + If[i>n || FactorInteger[i][[All, 1]] ~Intersection~ s != {}, 0, x*b[n-i, i-1, Select[s ~Union~ FactorInteger[i][[All, 1]], # <= i-1&]]*Binomial[n, i]]]];
a[n_] := b[n, n, {}] // CoefficientList[#, x]& // Total;
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 23 2017, translated from Maple *)
CROSSREFS
Row sums of A280880.
Sequence in context: A267400 A363064 A052302 * A009598 A355861 A002216
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 30 2016
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)