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

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 = 5..650

Crossrefs

Column k=5 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:=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 *)