A343669 Number of partitions of an n-set without blocks of size 9.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115965, 678460, 4212497, 27633712, 190795218, 1381942530, 10470109267, 82764226404, 681048663329, 5822029128397, 51610194855972, 473631475252041, 4492967510009533, 43996047374513046, 444151309687221889, 4617189912288741028

Offset

0,3

Links

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

Formula

E.g.f.: exp(exp(x) - 1 - x^9/9!).

a(n) = n! * Sum_{k=0..floor(n/9)} (-1)^k * Bell(n-9*k) / ((n-9*k)! * k! * (9!)^k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=9, 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^9/9!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 9 k]/((n - 9 k)! k! (9!)^k), {k, 0, Floor[n/9]}], {n, 0, 25}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 9, 0, Binomial[n - 1, k - 1]  a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000110, A000296, A027343, A097514, A124504, A343664, A343665, A343666, A343667, A343668.

Sequence in context: A366775 A192865 A229225 * A276725 A287587 A287280

Adjacent sequences: A343666 A343667 A343668 * A343670 A343671 A343672

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2021

Status

approved