A343671 Number of partitions of an n-set without blocks of size 10.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115974, 678559, 4213465, 27643007, 190884307, 1382802389, 10478516523, 82847813908, 681895648039, 5830788687491, 51702731250650, 474630475600569, 4503991075480297, 44120379612630694, 445584481578266277, 4634070027874688433

Offset

0,3

Links

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

Formula

E.g.f.: exp(exp(x) - 1 - x^10/10!).

a(n) = n! * Sum_{k=0..floor(n/10)} (-1)^k * Bell(n-10*k) / ((n-10*k)! * k! * (10!)^k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
       j=10, 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Jul 25 2023

Mathematica

nmax = 25; CoefficientList[Series[Exp[Exp[x] - 1 - x^10/10!], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^k BellB[n - 10 k]/((n - 10 k)! k! (10!)^k), {k, 0, Floor[n/10]}], {n, 0, 25}]
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 10, 0, Binomial[n - 1, k - 1]  a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000110, A000296, A027344, A097514, A124504, A343664, A343665, A343666, A343667, A343668, A343669.

Sequence in context: A164863 A192126 A229226 * A276726 A287588 A287281

Adjacent sequences: A343668 A343669 A343670 * A343672 A343673 A343674

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 25 2021

Status

approved