A243740 Number of compositions of n with exactly five occurrences of the largest part.

1, 0, 0, 0, 0, 1, 6, 21, 56, 126, 253, 468, 819, 1385, 2317, 3928, 6908, 12803, 25079, 51415, 108598, 232784, 500780, 1073700, 2285703, 4822956, 10082161, 20884730, 42892750, 87405633, 176867184, 355685658, 711460052, 1416584340, 2809770487, 5555833511

Offset

5,7

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 5..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:=5;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=5..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=5; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 5, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)

Crossrefs

Column k=5 of A238341.

Sequence in context: A019500 A100356 A229886 * A369794 A137361 A058484

Adjacent sequences: A243737 A243738 A243739 * A243741 A243742 A243743

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved