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A243737
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Number of compositions of n with exactly two occurrences of the largest part.
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8
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1, 0, 1, 3, 7, 13, 25, 46, 89, 175, 351, 710, 1443, 2926, 5920, 11936, 23987, 48072, 96139, 191977, 382992, 763686, 1522581, 3035979, 6055454, 12082887, 24120923, 48174935, 96259627, 192418152, 384772810, 769651514, 1539889604, 3081525905, 6167365392
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OFFSET
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2,4
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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:=2;
add(b(n-i*k, k, i-1)/k!, i=1..n/k)
end:
seq(a(n), n=2..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=2; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]) ; Table[ a[n], {n, 2, 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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