%I
%S 1,1,1,2,1,2,1,4,3,2,1,4,1,2,3,8,1,6,1,4,3,2,1,8,4,2,9,4,1,6,1,16,3,2,
%T 4,12,1,2,3,8,1,6,1,4,9,2,1,16,5,8,3,4,1,18,4,8,3,2,1,12,1,2,9,32,4,6,
%U 1,4,3,8,1,24,1,2,12,4,5,6,1,16,27,2,1
%N Number of unimodal negated permutations of a multiset whose multiplicities are the prime indices of n.
%C This multiset is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
%C A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnimodalSequence.html">Unimodal Sequence</a>
%F a(n) + A332742(n) = A318762(n).
%e The a(12) = 4 permutations:
%e {1,1,2,3}
%e {2,1,1,3}
%e {3,1,1,2}
%e {3,2,1,1}
%t nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
%t Table[Length[Select[Permutations[nrmptn[n]],unimodQ[#]&]],{n,30}]
%Y Dominated by A318762.
%Y The nonnegated version is A332294.
%Y The complement is counted by A332742.
%Y A less interesting version is A333145.
%Y Unimodal compositions are A001523.
%Y Unimodal normal sequences are A007052.
%Y Numbers with nonunimodal negated prime signature are A332642.
%Y Partitions whose 0appended first differences are unimodal are A332283.
%Y Compositions whose negation is unimodal are A332578.
%Y Partitions with unimodal negated runlengths are A332638.
%Y Cf. A056239, A112798, A115981, A124010, A181819, A181821, A304660, A332280, A332288, A332639, A332669, A332672.
%K nonn
%O 1,4
%A _Gus Wiseman_, Mar 09 2020
