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A243738
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Number of compositions of n with exactly three occurrences of the largest part.
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2
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1, 0, 0, 1, 4, 10, 21, 39, 70, 125, 229, 435, 859, 1739, 3574, 7384, 15239, 31312, 63968, 129898, 262316, 527169, 1055254, 2105849, 4192933, 8335832, 16557580, 32877010, 65286137, 129695835, 257817166, 512918318, 1021351641, 2035674817, 4061093104, 8108844651
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OFFSET
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3,5
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LINKS
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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:=3;
add(b(n-i*k, k, i-1)/k!, i=1..n/k)
end:
seq(a(n), n=3..40);
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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=3; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)
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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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