A341283 Number of ways to partition n labeled elements into sets of different sizes of at least 3.

1, 0, 0, 1, 1, 1, 1, 36, 57, 211, 331, 958, 29228, 64065, 294659, 1232479, 3549717, 11296603, 557617987, 1512758550, 8514685860, 41183585167, 251022906729, 838303110637, 4183056225010, 263978773601641, 887708421995331, 5813843897797861, 32212405278588967, 216518890998518716

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..699

Formula

E.g.f.: Product_{k>=3} (1 + x^k/k!).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
     `if`(i>n, 0, b(n, i+1)+b(n-i, i+1)*binomial(n, i)))
    end:
a:= n-> b(n, 3):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 28 2021

Mathematica

nmax = 29; CoefficientList[Series[Product[(1 + x^k/k!), {k, 3, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -(n - 1)! Sum[DivisorSum[k, # (-#!)^(-k/#) &, # > 2 &] a[n - k]/(n - k)!, {k, 1, n}]; Table[a[n], {n, 0, 29}]

Crossrefs

Cf. A006505, A007837, A025148, A032311, A102233, A343319, A343542.

Sequence in context: A116321 A187989 A080469 * A260138 A260131 A320632

Adjacent sequences: A341280 A341281 A341282 * A341284 A341285 A341286

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 28 2021

Status

approved