A097965 Number of compositions (ordered partitions) of n into n parts, allowing zeros, with distinct nonzero parts.

1, 2, 9, 16, 45, 186, 343, 848, 1809, 8290, 13431, 33672, 66157, 143066, 591165, 966016, 2180913, 4281570, 8776423, 15865400, 67586841, 101053282, 226690047, 420479952, 845781625, 1476079826, 2830894353, 10479645568, 15758982597, 33145324410, 60465162751

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maple

b:= proc(n, i) option remember; `if`(n=0, [1],
      `if`(n>i*(i+1)/2, [], zip((x, y)->x+y, b(n, i-1),
      `if`(i>n, [], [0, b(n-i, i-1)[]]), 0)))
    end:
a:= proc(n) local l; l:= b(n$2);
      add(l[i+1]*i!*binomial(n, i), i=1..nops(l)-1)
    end:
seq (a(n), n=1..40);  # Alois P. Heinz, Nov 20 2012

Mathematica

zip[f_, x_List, y_List, z_] := With[{m = Max[Length[x], Length[y]]}, Thread[f[PadRight[x, m, z], PadRight[y, m, z]]]]; b[n_, i_] := b[n, i] = If[n == 0, {1}, If[n > i*(i+1)/2, {}, zip[Plus, b[n, i-1], If[i>n, {}, Join[{0}, b[n-i, i-1]]], 0]]]; a[n_] := Module[{l}, l = b[n, n]; Sum[l[[i+1]]*i!*Binomial[n, i], {i, 1, Length[l]-1}]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 29 2014, after Alois P. Heinz *)

Crossrefs

Cf. A088218, A032020.

Sequence in context: A304907 A237282 A178440 * A304974 A075645 A185252

Adjacent sequences: A097962 A097963 A097964 * A097966 A097967 A097968

Keyword

nonn

Author

Vladeta Jovovic, Sep 21 2004

Status

approved