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

7,9

Links

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

Crossrefs

Column k=7 of A238341.

Sequence in context: A000580 A290995 A229888 * A145457 A145136 A290892

Adjacent sequences: A243739 A243740 A243741 * A243743 A243744 A243745

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved