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A336875
Number of parts, counted without multiplicity, in all compositions of n.
6
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
0,3
LINKS
EXAMPLE
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).
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 *)
CROSSREFS
Cf. A000070 (the same for partitions), A001792 (all parts), A097910, A336516.
Sequence in context: A115217 A094687 A369584 * A219753 A239305 A018013
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2020
STATUS
approved