A325510 Number of non-isomorphic multiset partitions of the multiset of prime indices of n!.

1, 1, 1, 2, 7, 16, 98, 269, 1397, 7582, 70520, 259906, 1677259, 5229112, 44726100, 666355170, 4917007185, 18459879921

Offset

0,4

Links

Table of n, a(n) for n=0..17.

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

Crossrefs

Cf. A000142, A001055, A007716, A011371, A022559, A076716, A115627, A317791, A318285, A322583, A325272, A325276, A325508, A325509, A325511.

Sequence in context: A129444 A079815 A362760 * A347601 A006883 A023269

Adjacent sequences: A325507 A325508 A325509 * A325511 A325512 A325513

Keyword

nonn,more

Author

Gus Wiseman, May 08 2019

Extensions

a(9)-a(17) from Andrew Howroyd, Jan 17 2023

Status

approved