A364450 Number of partitions of [n] without prime sized blocks.

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

Author

Alois P. Heinz, Jul 25 2023

Keywords

• nonn

Examples

			a(4) = 2: 1|2|3|4, 1234.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..592

Crossrefs

Cf. A000040, A097514, A190476, A329944.

Programs

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);

Formula

E.g.f.: exp(exp(x)-1-Sum_{p in primes} x^p/p!).