login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341283 Number of ways to partition n labeled elements into sets of different sizes of at least 3. 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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)