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A364450
Number of partitions of [n] without prime sized blocks.
3
1, 1, 1, 1, 2, 6, 17, 43, 135, 536, 2262, 9109, 40119, 198069, 1057149, 5656915, 31937212, 191032078, 1218669125, 7948119483, 54117500635, 381631039690, 2828205076600, 21507011811289, 169880627954541, 1377653319819302, 11620433411120653, 100417638302823210
OFFSET
0,5
LINKS
FORMULA
E.g.f.: exp(exp(x)-1-Sum_{p in primes} x^p/p!).
EXAMPLE
a(4) = 2: 1|2|3|4, 1234.
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
isprime(j), 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
end:
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 25 2023
STATUS
approved