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A243743
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Number of compositions of n with exactly eight occurrences of the largest part.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 1, 9, 45, 165, 495, 1287, 3003, 6435, 12871, 24319, 43812, 75837, 127005, 207252, 332343, 529617, 851797, 1410484, 2456794, 4572624, 9116790, 19248417, 42237738, 94608183, 213426424, 480788350, 1076330078, 2388681769, 5249788389
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OFFSET
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8,10
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LINKS
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Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..650
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MAPLE
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b:= proc(n, p, i) option remember; `if`(n=0, p!,
`if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))
end:
a:= proc(n) local k; k:=8;
add(b(n-i*k, k, i-1)/k!, i=1..n/k)
end:
seq(a(n), n=8..50);
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MATHEMATICA
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b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=8; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 8, 50}] (* Jean-François Alcover, Feb 10 2015, after Maple *)
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CROSSREFS
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Column k=8 of A238341.
Sequence in context: A000581 A306939 A229889 * A145458 A145137 A221142
Adjacent sequences: A243740 A243741 A243742 * A243744 A243745 A243746
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt and Alois P. Heinz, Jun 09 2014
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STATUS
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approved
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