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A272519
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Number of set partitions of [n] into seven blocks with distinct sizes.
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2
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2431106898187968000, 8812762505931384000, 67144857188048640000, 416298114565901568000, 3144312274410635328000, 23728992530256389376000, 238675412699786289427200, 3207620559498676985664000, 16207982672116390803648000, 117220515926387332979520000
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OFFSET
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28,1
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LINKS
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FORMULA
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a(n) = n! * [x^n*y^7] Product_{n>=1} (1+y*x^n/n!).
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MAPLE
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b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n, i))))
end:
a:= n-> b(n$2, 7):
seq(a(n), n=28..40);
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[t > i || t*(t + 1)/2 > n || t*(2*i + 1 - t)/2 < n, 0, If[n == 0, 1, b[n, i - 1, t] + If[i > n, 0, b[n - i, i - 1, t - 1]*Binomial[n, i]]]];
a[n_] := b[n, n, 7];
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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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