A343664 Number of partitions of an n-set without blocks of size 4.

1, 1, 2, 5, 14, 47, 173, 702, 3125, 14910, 76495, 418035, 2418397, 14791597, 95093612, 641094695, 4521228732, 33250447919, 254585084539, 2024995604762, 16702070759557, 142642458681486, 1259387604241013, 11479967000116911, 107910143688962037, 1044735841257587203, 10407104137208385924

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..581

Formula

E.g.f.: exp(exp(x) - 1 - x^4/4!).

a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * Bell(n-4*k) / ((n-4*k)! * k! * (4!)^k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=4, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
    end:
seq(a(n), n=0..26);  # Alois P. Heinz, Apr 25 2021

Mathematica

nmax = 26; CoefficientList[Series[Exp[Exp[x] - 1 - x^4/4!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 4 k]/((n - 4 k)! k! (4!)^k), {k, 0, Floor[n/4]}], {n, 0, 26}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n - 1, k - 1]  a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A000110, A000296, A027338, A097514, A124504, A343665, A343666, A343667, A343668, A343669.

Sequence in context: A149904 A287888 A115276 * A327702 A317784 A096402

Adjacent sequences: A343661 A343662 A343663 * A343665 A343666 A343667

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2021

Status

approved