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%I #11 Mar 23 2018 20:52:58
%S 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,
%T 83,78,54,19,7,2,1,30,120,168,102,54,19,7,2,1,42,223,301,244,134,54,
%U 19,7,2,1,56,320,557,471,292,134,54,19,7,2,1,77,566,1035,1000,623,356,134,54
%N Triangle read by rows: row n lists number of unordered partitions of n into k parts which are partition numbers (members of A000041).
%C A060642 describes the ordered case.
%C 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
%F G.f.: 1/Product_{k>0} (1-y*A000041(k)*x^k). - _Vladeta Jovovic_, May 21 2006
%e Triangle begins:
%e 1
%e 2 1
%e 3 2 1
%e 5 7 2 1
%e 7 11 7 2 1
%e 11 26 19 7 2 1
%e 15 40 38 19 7 2 1
%e 22 83 78 54 19 7 2 1
%e 30 120 168 102 54 19 7 2 1
%e 42 223 301 244 134 54 19 7 2 1
%e 56 320 557 471 292 134 54 19 7 2 1
%e 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
%t nn=12;
%t ser=Product[1/(1-PartitionsP[n]x^n y),{n,nn}];
%t Table[SeriesCoefficient[ser,{x,0,n},{y,0,k}],{n,nn},{k,n}] (* _Gus Wiseman_, Mar 23 2018 *)
%Y Cf. A000041, A001970, A008284, A036036, A048996, A055887, A061260, A063834, A273873, A281145, A289501, A299200, A299201.
%K nonn,tabl
%O 0,2
%A _Alford Arnold_, May 19 2006
%E More terms and better definition from _Vladeta Jovovic_, May 21 2006
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