OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2313
FORMULA
a(n) = Sum_{k=1..n} k * A060642(n,k).
a(n) ~ c * d^n * n, where d = A246828 = 2.69832910647421123126399866618837633... and c = 0.171490233695958246364725709205670983251448838158816... - Vaclav Kotesovec, Sep 14 2019
EXAMPLE
a(3) = 14 = 1+1+1+2+2+2+2+3 counts the partitions in 3, 21, 111, 2|1, 11|1, 1|2, 1|11, 1|1|1.
MAPLE
b:= proc(n) option remember; `if`(n=0, [1, 0], (p-> p+
[0, p[1]])(add(combinat[numbpart](j)*b(n-j), j=1..n)))
end:
a:= n-> b(n)[2]:
seq(a(n), n=0..32);
MATHEMATICA
b[n_] := b[n] = If[n==0, {1, 0}, Function[p, p + {0, p[[1]]}][Sum[ PartitionsP[j] b[n-j], {j, 1, n}]]];
a[n_] := b[n][[2]];
a /@ Range[0, 32] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 11 2019
STATUS
approved