OFFSET
10,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 10..576
Wikipedia, Partition of a set
FORMULA
a(n) = Bell(n+1) - Sum_{j=0..9} binomial(n,j) * Bell(n-j).
a(n) = Sum_{j=0..n-10} binomial(n,j) * Bell(j).
E.g.f.: (exp(x) - Sum_{k=0..9} x^k/k!) * exp(exp(x) - 1). - Ilya Gutkovskiy, Jun 26 2022
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1), j=1..n))
end:
g:= proc(n, k) option remember; `if`(n<k, 0,
g(n, k+1) +binomial(n, k)*b(n-k))
end:
a:= n-> g(n, 10):
seq(a(n), n=10..30);
MATHEMATICA
Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 10}], {n, 10, 30}] (* Indranil Ghosh, Jul 06 2017 *)
PROG
(Python)
from sympy import bell, binomial
def a(n): return sum([binomial(n, j)*bell(j) for j in range(n - 9)])
print([a(n) for n in range(10, 31)]) # Indranil Ghosh, Jul 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 15 2017
STATUS
approved