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A320739
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Number of partitions of n with eight sorts of part 1 which are introduced in ascending order.
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4
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1, 1, 3, 7, 20, 63, 233, 966, 4454, 22403, 121570, 705150, 4337883, 28091897, 190105229, 1334705996, 9656244012, 71551215515, 540187472767, 4137336876098, 32036946594336, 250131019258467, 1965050543015106, 15509209887539395, 122829846706462146
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1112
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..8), add(b(n-i*j, i-1), j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 8}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
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CROSSREFS
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Column k=8 of A292745.
Sequence in context: A320736 A320737 A320738 * A320740 A320741 A292503
Adjacent sequences: A320736 A320737 A320738 * A320740 A320741 A320742
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 20 2018
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STATUS
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approved
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