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A370365
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Total sum over all j in [n] of the number of partitions of [j*(n-j)] into (n-j) sets of size j having at least one set of consecutive numbers whose maximum (if j>0) is a multiple of j.
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4
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0, 1, 2, 3, 4, 11, 77, 1571, 101924, 21824842, 18998281193, 63437859518312, 1037654210033812290, 72422876152852051595343, 27306605231809196751929593081, 50723306700937648229840111395656830, 510196838745355443955126736574361550469276
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} A370363(j,n-j).
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MAPLE
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b:= proc(n, k) option remember; `if`(k=0, signum(n), add(
(-1)^(n-j+1)*binomial(n, j)*(k*j)!/(j!*k!^j), j=0..n-1))
end:
a:= n-> add(b(j, n-j), j=0..n):
seq(a(n), n=0..16);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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