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

%I A364450 #12 Jul 25 2023 09:24:07
%S A364450 1,1,1,1,2,6,17,43,135,536,2262,9109,40119,198069,1057149,5656915,
%T A364450 31937212,191032078,1218669125,7948119483,54117500635,381631039690,
%U A364450 2828205076600,21507011811289,169880627954541,1377653319819302,11620433411120653,100417638302823210
%N A364450 Number of partitions of [n] without prime sized blocks.
%H A364450 Alois P. Heinz, <a href="/A364450/b364450.txt">Table of n, a(n) for n = 0..592</a>
%F A364450 E.g.f.: exp(exp(x)-1-Sum_{p in primes} x^p/p!).
%e A364450 a(4) = 2: 1|2|3|4, 1234.
%p A364450 a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
%p A364450       isprime(j), 0, a(n-j)*binomial(n-1, j-1)), j=1..n))
%p A364450     end:
%p A364450 seq(a(n), n=0..30);
%Y A364450 Cf. A000040, A097514, A190476, A329944.
%K A364450 nonn
%O A364450 0,5
%A A364450 _Alois P. Heinz_, Jul 25 2023