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A326026 Number of non-isomorphic multiset partitions of weight n where each part has a different length.

%I A326026 #8 Feb 08 2020 20:41:55
%S A326026 1,1,2,7,12,35,111,247,624,1843,6717,15020,46847,124808,412577,
%T A326026 1658973,4217546,12997734,40786810,126971940,437063393,2106317043,
%U A326026 5499108365,19037901867,59939925812,210338815573,683526043801,2741350650705,14848209030691,41533835240731,151548411269815
%N A326026 Number of non-isomorphic multiset partitions of weight n where each part has a different length.
%C A326026 The number of non-isomorphic multiset partitions of weight n is A007716(n).
%H A326026 Andrew Howroyd, <a href="/A326026/b326026.txt">Table of n, a(n) for n = 0..50</a>
%e A326026 Non-isomorphic representatives of the a(1) = 1 through a(4) = 12 multiset partitions:
%e A326026   {{1}}  {{1,1}}  {{1,1,1}}    {{1,1,1,1}}
%e A326026          {{1,2}}  {{1,2,2}}    {{1,1,2,2}}
%e A326026                   {{1,2,3}}    {{1,2,2,2}}
%e A326026                   {{1},{1,1}}  {{1,2,3,3}}
%e A326026                   {{1},{2,2}}  {{1,2,3,4}}
%e A326026                   {{1},{2,3}}  {{1},{1,1,1}}
%e A326026                   {{2},{1,2}}  {{1},{1,2,2}}
%e A326026                                {{1},{2,2,2}}
%e A326026                                {{1},{2,3,3}}
%e A326026                                {{1},{2,3,4}}
%e A326026                                {{2},{1,2,2}}
%e A326026                                {{3},{1,2,3}}
%o A326026 (PARI)
%o A326026 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A326026 D(p,n)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); my(u=EulerT(v)); polcoef(prod(k=1, #u, 1 + u[k]*x^k + O(x*x^n)), n)/prod(i=1, #v, i^v[i]*v[i]!)}
%o A326026 a(n)={my(s=0); forpart(p=n, s+=D(p,n)); s} \\ _Andrew Howroyd_, Feb 08 2020
%Y A326026 Row sums of A332260.
%Y A326026 Cf. A007716, A007837, A303546, A306017, A316980, A316983, A319560, A326514, A326517, A326533.
%K A326026 nonn
%O A326026 0,3
%A A326026 _Gus Wiseman_, Jul 13 2019
%E A326026 Terms a(11) and beyond from _Andrew Howroyd_, Feb 08 2020