A243742 Number of compositions of n with exactly seven occurrences of the largest part.

1, 0, 0, 0, 0, 0, 0, 1, 8, 36, 120, 330, 792, 1716, 3433, 6443, 11484, 19640, 32550, 52860, 85296, 139249, 235001, 418473, 795544, 1610418, 3421514, 7489962, 16625389, 37003313, 82024320, 180421399, 393126594, 848051064, 1811227670, 3831269241, 8030748161

Offset: 7

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Keywords

• nonn

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 7..650

Crossrefs

Column k=7 of A238341.

Programs

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:=7;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=7..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=7; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 7, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)