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A325510
Number of non-isomorphic multiset partitions of the multiset of prime indices of n!.
2
1, 1, 1, 2, 7, 16, 98, 269, 1397, 7582, 70520, 259906, 1677259, 5229112, 44726100, 666355170, 4917007185, 18459879921
OFFSET
0,4
FORMULA
a(n) = A317791(n!).
a(n) = A318285(A181819(n!)) = A318285(A325508(n)). - Andrew Howroyd, Jan 17 2023
EXAMPLE
Non-isomorphic representatives of the a(2) = 1 through a(5) = 16 multiset partitions:
{{1}} {{12}} {{1222}} {{12333}}
{{1}{2}} {{1}{222}} {{1}{2333}}
{{12}{22}} {{12}{333}}
{{2}{122}} {{13}{233}}
{{1}{2}{22}} {{3}{1233}}
{{2}{2}{12}} {{33}{123}}
{{1}{2}{2}{2}} {{1}{2}{333}}
{{1}{23}{33}}
{{1}{3}{233}}
{{3}{12}{33}}
{{3}{13}{23}}
{{3}{3}{123}}
{{1}{1}{1}{23}}
{{1}{2}{3}{33}}
{{1}{3}{3}{23}}
{{1}{2}{3}{3}{3}}
PROG
(PARI) \\ Requires C(sig) from A318285.
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 08 2019
EXTENSIONS
a(9)-a(17) from Andrew Howroyd, Jan 17 2023
STATUS
approved