A243743 Number of compositions of n with exactly eight occurrences of the largest part.

1, 0, 0, 0, 0, 0, 0, 0, 1, 9, 45, 165, 495, 1287, 3003, 6435, 12871, 24319, 43812, 75837, 127005, 207252, 332343, 529617, 851797, 1410484, 2456794, 4572624, 9116790, 19248417, 42237738, 94608183, 213426424, 480788350, 1076330078, 2388681769, 5249788389

Offset

8,10

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..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:=8;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=8..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=8; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 8, 50}] (* Jean-François Alcover, Feb 10 2015, after Maple *)

Crossrefs

Column k=8 of A238341.

Sequence in context: A000581 A306939 A229889 * A145458 A145137 A221142

Adjacent sequences: A243740 A243741 A243742 * A243744 A243745 A243746

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved