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 A066815 Number of partitions of n into sums of products. 14
 1, 1, 2, 3, 6, 8, 14, 19, 33, 45, 69, 94, 148, 197, 289, 390, 575, 762, 1086, 1439, 2040, 2687, 3712, 4874, 6749, 8792, 11918, 15526, 20998, 27164, 36277, 46820, 62367, 80146, 105569, 135326, 177979, 227139, 296027, 377142, 490554, 622526, 804158 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of ways to choose a factorization of each part of an integer partition of n. - Gus Wiseman, Sep 05 2018 This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1, g(n) = A001055(n). - Seiichi Manyama, Nov 14 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{k>=1} 1/(1-A001055(k)*x^k). a(n) = 1/n*Sum_{k=1..n} a(n-k)*b(k), n > 0, a(0)=1, b(k)=Sum_{d|k} d*(A001055(d))^(k/d). EXAMPLE From Gus Wiseman, Sep 05 2018: (Start) The a(6) = 14 partitions of 6 into sums of products:   6, 2*3,   5+1, 4+2, 2*2+2, 3+3,   4+1+1, 2*2+1+1, 3+2+1, 2+2+2,   3+1+1+1, 2+2+1+1,   2+1+1+1+1,   1+1+1+1+1+1. (End) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]]; Table[Length[Join@@Table[Tuples[facs/@ptn], {ptn, IntegerPartitions[n]}]], {n, 20}] (* Gus Wiseman, Sep 05 2018 *) CROSSREFS Cf. A000041, A001055, A066739, A321460. Cf. A001970, A050336, A063834, A065026, A281113, A284639, A318948, A318949. Sequence in context: A321360 A321566 A066739 * A106182 A097097 A283474 Adjacent sequences:  A066812 A066813 A066814 * A066816 A066817 A066818 KEYWORD nonn AUTHOR Vladeta Jovovic, Jan 20 2002 EXTENSIONS Renamed by T. D. Noe, May 24 2011 STATUS approved

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Last modified May 25 21:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)