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A243740
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Number of compositions of n with exactly five occurrences of the largest part.
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2
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1, 0, 0, 0, 0, 1, 6, 21, 56, 126, 253, 468, 819, 1385, 2317, 3928, 6908, 12803, 25079, 51415, 108598, 232784, 500780, 1073700, 2285703, 4822956, 10082161, 20884730, 42892750, 87405633, 176867184, 355685658, 711460052, 1416584340, 2809770487, 5555833511
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OFFSET
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5,7
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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:=5;
add(b(n-i*k, k, i-1)/k!, i=1..n/k)
end:
seq(a(n), n=5..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=5; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 5, 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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