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A132963
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Total number of distinct block sizes in all partitions of [n].
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7
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1, 2, 8, 25, 102, 439, 2067, 10406, 56754, 328257, 2015818, 13067366, 89192170, 638321285, 4779442602, 37332643831, 303635437532, 2565592977205, 22483754207839, 204013083946460, 1913880812797792, 18536832515581167, 185130415180288134, 1904280138346826637
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: exp(exp(x)-1)*Sum_{k>0} (1-exp(-x^k/k!)).
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MAPLE
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b:= proc(n, i, c) option remember; `if`(n=0, c,
`if`(i<1, 0, add(b(n-j*i, i-1, c+signum(j))*
combinat[multinomial](n, n-i*j, i$j)/j!, j=0..n/i)))
end:
a:= n-> b(n$2, 0):
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MATHEMATICA
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Rest[ Range[0, 23]! CoefficientList[ Series[ Exp[ Exp[x] - 1] Sum[1 - Exp[ -x^k/k! ], {k, 30}], {x, 0, 23}], x]] (* Robert G. Wilson v, Sep 13 2007 *)
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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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EXTENSIONS
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STATUS
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approved
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