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A325929
Total number of sub-subsets of set partitions of [n] where each subset is again partitioned into nonempty subsets.
2
0, 1, 4, 14, 57, 262, 1326, 7499, 47662, 334794, 2555639, 21124116, 189492474, 1838561337, 19094196270, 210014919406, 2433655645025, 29707254349866, 382324345380310, 5179102279125987, 73515985821539778, 1087888385861343158, 16724494503770495231
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} k * A324162(n,k).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0 or k>n, 0,
add(b(n-j, k)*binomial(n-1, j-1)*Stirling2(j, k), j=k..n)))
end:
a:= n-> add(b(n, k)*k, k=0..n):
seq(a(n), n=0..23);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n - j, k] Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];
a[n_] := Sum[b[n, k] k, {k, 0, n}];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)
CROSSREFS
Cf. A324162.
Sequence in context: A269134 A186828 A151489 * A134826 A096242 A360198
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2019
STATUS
approved