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A368102
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Total number of partitions of [n-s] whose block maxima sum to s, summed over all s.
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3
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1, 0, 1, 0, 1, 1, 1, 1, 3, 2, 3, 6, 5, 9, 14, 13, 20, 40, 31, 56, 86, 105, 127, 227, 244, 394, 520, 665, 911, 1536, 1565, 2449, 3507, 4719, 5931, 9061, 11151, 16911, 21774, 29798, 39804, 60411, 71865, 104399, 144999, 197907, 253430, 370044, 478764, 694807
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OFFSET
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0,9
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LINKS
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EXAMPLE
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a(11) = 6: 123|4, 124|3, 13|24, 14|23, 1|2|34, 1|2345.
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0, 1,
b(n-1, m)*m + expand(x^n*b(n-1, m+1)))
end:
a:= n-> add(coeff(b(n-k, 0), x, k), k=ceil(n/2)..n):
seq(a(n), n=0..80);
# second Maple program:
b:= proc(n, i, t) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, t^i, `if`(t=0, 0, t*b(n, i-1, t))+
(t+1)^max(0, 2*i-n-1)*b(n-i, min(n-i, i-1), t+1)))
end:
a:= n-> add(b(k, n-k, 0), k=ceil(n/2)..n):
seq(a(n), n=0..80);
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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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