A343542 Number of ways to partition n labeled elements into sets of different sizes of at least 5.

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 463, 793, 3004, 5006, 14444, 23817, 62323, 14805403, 35175993, 177791475, 745977222, 2333540804, 7589340982, 29027728612, 81515120641, 23232813583331, 69799133324911, 436678552247551, 2215090972333651, 13529994077951557, 48863594588239153

Offset

0,12

Links

Alois P. Heinz, Table of n, a(n) for n = 0..700

Formula

E.g.f.: Product_{k>=5} (1 + x^k/k!).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
     `if`(i>n, 0, b(n, i+1)+binomial(n, i)*b(n-i, i+1)))
    end:
a:= n-> b(n, 5):
seq(a(n), n=0..31);  # Alois P. Heinz, Apr 28 2021

Mathematica

nmax = 31; CoefficientList[Series[Product[(1 + x^k/k!), {k, 5, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -(n - 1)! Sum[DivisorSum[k, # (-#!)^(-k/#) &, # > 4 &] a[n - k]/(n - k)!, {k, 1, n}]; Table[a[n], {n, 0, 31}]

Crossrefs

Cf. A007837, A025150, A032311, A057814, A245790, A341283, A343319.

Sequence in context: A020371 A234842 A116323 * A142282 A270760 A293025

Adjacent sequences: A343539 A343540 A343541 * A343543 A343544 A343545

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 28 2021

Status

approved