A243744 Number of compositions of n with exactly nine occurrences of the largest part.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48621, 92388, 168025, 294260, 498850, 822712, 1327029, 2107325, 3324750, 5280276, 8595025, 14648920, 26637015, 52076915, 108669142, 237787000, 535084341, 1219016810, 2782344676

Offset

9,11

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..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:=9;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=9..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=9; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 9, 50}] (* Jean-François Alcover, Feb 10 2015, after Maple *)

Crossrefs

Column k=9 of A238341.

Sequence in context: A128936 A000582 A229890 * A145459 A290893 A034241

Adjacent sequences: A243741 A243742 A243743 * A243745 A243746 A243747

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved