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A343669 Number of partitions of an n-set without blocks of size 9. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A366775 A192865 A229225 * A276725 A287587 A287280
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2021
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)