A364450 - OEIS

%I #12 Jul 25 2023 09:24:07

%S 1,1,1,1,2,6,17,43,135,536,2262,9109,40119,198069,1057149,5656915,

%T 31937212,191032078,1218669125,7948119483,54117500635,381631039690,

%U 2828205076600,21507011811289,169880627954541,1377653319819302,11620433411120653,100417638302823210

%N Number of partitions of [n] without prime sized blocks.

%H Alois P. Heinz, <a href="/A364450/b364450.txt">Table of n, a(n) for n = 0..592</a>

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

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

%p a:= proc(n) option remember; `if`(n=0, 1, add(`if`(

%p       isprime(j), 0, a(n-j)*binomial(n-1, j-1)), j=1..n))

%p     end:

%p seq(a(n), n=0..30);

%Y Cf. A000040, A097514, A190476, A329944.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jul 25 2023