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%I #9 Jan 17 2023 21:24:34
%S 1,1,1,2,7,16,98,269,1397,7582,70520,259906,1677259,5229112,44726100,
%T 666355170,4917007185,18459879921
%N Number of non-isomorphic multiset partitions of the multiset of prime indices of n!.
%F a(n) = A317791(n!).
%F a(n) = A318285(A181819(n!)) = A318285(A325508(n)). - _Andrew Howroyd_, Jan 17 2023
%e Non-isomorphic representatives of the a(2) = 1 through a(5) = 16 multiset partitions:
%e {{1}} {{12}} {{1222}} {{12333}}
%e {{1}{2}} {{1}{222}} {{1}{2333}}
%e {{12}{22}} {{12}{333}}
%e {{2}{122}} {{13}{233}}
%e {{1}{2}{22}} {{3}{1233}}
%e {{2}{2}{12}} {{33}{123}}
%e {{1}{2}{2}{2}} {{1}{2}{333}}
%e {{1}{23}{33}}
%e {{1}{3}{233}}
%e {{3}{12}{33}}
%e {{3}{13}{23}}
%e {{3}{3}{123}}
%e {{1}{1}{1}{23}}
%e {{1}{2}{3}{33}}
%e {{1}{3}{3}{23}}
%e {{1}{2}{3}{3}{3}}
%o (PARI) \\ Requires C(sig) from A318285.
%o a(n)={if(n<2, 1, my(f=factor(n!)[,2], sig=vector(vecmax(f))); for(i=1, #f, sig[f[i]]++); C(sig))} \\ _Andrew Howroyd_, Jan 17 2023
%Y Cf. A000142, A001055, A007716, A011371, A022559, A076716, A115627, A317791, A318285, A322583, A325272, A325276, A325508, A325509, A325511.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, May 08 2019
%E a(9)-a(17) from _Andrew Howroyd_, Jan 17 2023
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