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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

Table of n, a(n) for n=0..73.

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.)