A343666 Number of partitions of an n-set without blocks of size 6.

1, 1, 2, 5, 15, 52, 202, 870, 4084, 20727, 112825, 654546, 4026487, 26145511, 178550986, 1278168860, 9564026947, 74615547996, 605593775899, 5103054929621, 44564754448972, 402677613100491, 3759094788129312, 36205919126040190, 359340174509911325, 3670825700549853053

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

E.g.f.: exp(exp(x) - 1 - x^6/6!).

a(n) = n! * Sum_{k=0..floor(n/6)} (-1)^k * Bell(n-6*k) / ((n-6*k)! * k! * (6!)^k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=6, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Apr 25 2021

Mathematica

nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^6/6!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 6 k]/((n - 6 k)! k! (6!)^k), {k, 0, Floor[n/6]}], {n, 0, 25}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 6, 0, Binomial[n - 1, k - 1]  a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000110, A000296, A027340, A097514, A124504, A343664, A343665, A343667, A343668, A343669.

Sequence in context: A158829 A306551 A110038 * A276722 A287584 A287277

Adjacent sequences: A343663 A343664 A343665 * A343667 A343668 A343669

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2021

Status

approved