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A336516 Sum of parts, counted without multiplicity, in all compositions of n. 5
0, 1, 3, 10, 24, 59, 136, 309, 682, 1493, 3223, 6904, 14675, 31013, 65202, 136512, 284748, 592082, 1227709, 2539516, 5241640, 10798133, 22206568, 45597489, 93495667, 191464970, 391636718, 800233551, 1633530732, 3331568080, 6789078236, 13824212219, 28129459098 (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 + 1 + 2 + 1 + 2 + 1 + 2 + 2 + 1 + 3 + 3 + 1 + 4 = 24: (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]*i)]+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[Function[{0, If[j == 0, 0, #[[1]]*i]} + #][

b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];

a[n_] := b[n, n, 0][[2]];

Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Mar 11 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A001787 (all parts), A014153 (the same for partitions), A336511, A336512, A336579, A336875.

Sequence in context: A355024 A338706 A338710 * A286209 A293797 A179608

Adjacent sequences: A336513 A336514 A336515 * A336517 A336518 A336519

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 24 2020

STATUS

approved

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Last modified November 30 12:40 EST 2022. Contains 358441 sequences. (Running on oeis4.)