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A285370
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Sum of the entries in the eighth blocks of all set partitions of [n].
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2
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8, 333, 7995, 145814, 2250020, 31075944, 397434249, 4813480830, 56089581910, 636257739216, 7090058863984, 78176548855068, 858005254659222, 9419825826737075, 103885234357070729, 1154951013922367450, 12982852258320087936, 147928345019800310188
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OFFSET
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8,1
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LINKS
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FORMULA
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MAPLE
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a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=8, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=8..30);
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MATHEMATICA
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a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 8, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
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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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