A243745 Number of compositions of n with exactly ten occurrences of the largest part.

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

Offset

10,12

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 10..650

Maple

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);

Mathematica

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 *)

Crossrefs

Column k=10 of A238341.

Sequence in context: A008493 A001287 A229891 * A325752 A221143 A022576

Adjacent sequences: A243742 A243743 A243744 * A243746 A243747 A243748

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved