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A243745
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Number of compositions of n with exactly ten occurrences of the largest part.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184757, 352727, 646723, 1144484, 1963181, 3276625, 5341050, 8537815, 13454155, 21056035, 33090201, 53057236, 88592087, 157261599, 300524147, 616878471, 1339454952, 3015109174
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OFFSET
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10,12
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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:=10;
add(b(n-i*k, k, i-1)/k!, i=1..n/k)
end:
seq(a(n), n=10..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=10; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[ a[n], {n, 10, 50}] (* 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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