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 A321745 Sum of coefficients of monomial symmetric functions in the homogeneous symmetric function of the integer partition with Heinz number n. 1
 1, 1, 2, 3, 3, 6, 5, 10, 16, 12, 7, 27, 11, 20, 32, 47, 15, 76, 22, 56, 65, 35, 30, 136, 79, 54, 263, 114, 42, 191, 56, 246, 113, 86, 160, 476, 77, 128, 199, 344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). Also the number of size-preserving permutations of multiset partitions of a multiset (such as row n of A305936) whose multiplicities are the prime indices of n. LINKS Wikipedia, Symmetric polynomial EXAMPLE The sum of coefficients of h(211) = m(4) + 4m(22) + 3m(31) + 7m(211) + 12m(1111) is a(12) = 27. The a(3) = 2 through a(9) = 16 size-preserving permutations of multiset partitions: {11} {12} {111} {112} {1111} {123} {1122} {1}{1} {1}{2} {1}{11} {1}{12} {1}{111} {1}{23} {1}{122} {2}{1} {1}{1}{1} {2}{11} {11}{11} {2}{13} {11}{22} {1}{1}{2} {1}{1}{11} {3}{12} {12}{12} {1}{2}{1} {1}{1}{1}{1} {1}{2}{3} {2}{112} {2}{1}{1} {1}{3}{2} {22}{11} {2}{1}{3} {1}{1}{22} {2}{3}{1} {1}{2}{12} {3}{1}{2} {2}{1}{12} {3}{2}{1} {2}{2}{11} {1}{1}{2}{2} {1}{2}{1}{2} {1}{2}{2}{1} {2}{1}{1}{2} {2}{1}{2}{1} {2}{2}{1}{1} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Table[Sum[Times@@Factorial/@Length/@Split[Sort[Length/@mtn, Greater]]/Times@@Factorial/@Length/@Split[mtn], {mtn, mps[nrmptn[n]]}], {n, 30}] CROSSREFS Row sums of A321744. Cf. A005651, A007716, A008480, A056239, A124794, A124795, A181821, A255906, A296150, A318284, A319193, A319225, A319226, A321742-A321765. Sequence in context: A187754 A347732 A075258 * A212629 A127779 A207634 Adjacent sequences: A321742 A321743 A321744 * A321746 A321747 A321748 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 19 2018 STATUS approved

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Last modified January 29 10:45 EST 2023. Contains 359921 sequences. (Running on oeis4.)