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 A119442 Triangle read by rows: row n lists number of unordered partitions of n into k parts which are partition numbers (members of A000041). 4
 1, 2, 1, 3, 2, 1, 5, 7, 2, 1, 7, 11, 7, 2, 1, 11, 26, 19, 7, 2, 1, 15, 40, 38, 19, 7, 2, 1, 22, 83, 78, 54, 19, 7, 2, 1, 30, 120, 168, 102, 54, 19, 7, 2, 1, 42, 223, 301, 244, 134, 54, 19, 7, 2, 1, 56, 320, 557, 471, 292, 134, 54, 19, 7, 2, 1, 77, 566, 1035, 1000, 623, 356, 134, 54 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A060642 describes the ordered case. Number of twice-partitions of n of length k. A twice-partition of n is a choice of a partition of each part in a partition of n. - Gus Wiseman, Mar 23 2018 LINKS FORMULA G.f.: 1/Product_{k>0} (1-y*A000041(k)*x^k). - Vladeta Jovovic, May 21 2006 EXAMPLE Triangle begins:    1    2   1    3   2   1    5   7   2   1    7  11   7   2   1   11  26  19   7   2   1   15  40  38  19   7   2   1   22  83  78  54  19   7   2   1   30 120 168 102  54  19   7   2   1   42 223 301 244 134  54  19   7   2   1   56 320 557 471 292 134  54  19   7   2   1 The T(5,3) = 7 twice-partitions: (3)(1)(1), (21)(1)(1), (111)(1)(1), (2)(2)(1), (2)(11)(1), (11)(2)(1), (11)(11)(1). - Gus Wiseman, Mar 23 2018 MATHEMATICA nn=12; ser=Product[1/(1-PartitionsP[n]x^n y), {n, nn}]; Table[SeriesCoefficient[ser, {x, 0, n}, {y, 0, k}], {n, nn}, {k, n}] (* Gus Wiseman, Mar 23 2018 *) CROSSREFS Cf. A000041, A001970, A008284, A036036, A048996, A055887, A061260, A063834, A273873, A281145, A289501, A299200, A299201. Sequence in context: A134423 A061260 A152097 * A064861 A305299 A308701 Adjacent sequences:  A119439 A119440 A119441 * A119443 A119444 A119445 KEYWORD nonn,tabl AUTHOR Alford Arnold, May 19 2006 EXTENSIONS More terms and better definition from Vladeta Jovovic, May 21 2006 STATUS approved

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Last modified June 24 09:55 EDT 2019. Contains 324323 sequences. (Running on oeis4.)