A336875 Number of parts, counted without multiplicity, in all compositions of n.

0, 1, 2, 6, 13, 30, 66, 144, 308, 655, 1380, 2891, 6024, 12500, 25844, 53274, 109530, 224690, 460033, 940276, 1918979, 3911186, 7962194, 16191875, 32896364, 66776727, 135445212, 274532607, 556086916, 1125727954, 2277650681, 4605981879, 9310120876, 18810538092

Offset: 0

Author

Alois P. Heinz, Aug 06 2020

Keywords

• nonn

Examples

			a(4) = 1 + 2 + 2 + 2 + 1 + 2 + 2 + 1 = 13: (1)111, (1)1(2), (1)(2)1, (2)(1)1, (2)2, (1)(3), (3)(1), (4).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000070 (the same for partitions), A001792 (all parts), A097910, A336516.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
      `if`(i<1, 0, add((p-> [0, `if`(j=0, 0, p[1])]+p)(
         b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..38);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0},
     If[i<1, {0, 0}, Sum[{0, If[j == 0, 0, #[[1]]]}+#&[
     b[n-i*j, i-1, p+j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
a /@ Range[0, 38] (* Jean-François Alcover, Jun 13 2021, after Alois P. Heinz *)