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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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-Fran├žois Alcover, Jun 13 2021, after Alois P. Heinz *)

CROSSREFS

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

Sequence in context: A297388 A115217 A094687 * A219753 A239305 A018013

Adjacent sequences:  A336872 A336873 A336874 * A336876 A336877 A336878

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 06 2020

STATUS

approved

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Last modified August 7 19:55 EDT 2022. Contains 355994 sequences. (Running on oeis4.)