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Search: id:A060642
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| A060642 |
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Triangle read by rows: row n lists number of ordered partitions into k parts of partitions of n. |
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+0
3
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| 1, 2, 1, 3, 4, 1, 5, 10, 6, 1, 7, 22, 21, 8, 1, 11, 43, 59, 36, 10, 1, 15, 80, 144, 124, 55, 12, 1, 22, 141, 321, 362, 225, 78, 14, 1, 30, 240, 669, 944, 765, 370, 105, 16, 1, 42, 397, 1323, 2266, 2287, 1437, 567, 136, 18, 1, 56, 640, 2511, 5100, 6215, 4848, 2478, 824
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums give A055887
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FORMULA
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G.f. A(n;x) for n-th row satisfies A(n;x) = Sum_{k=0..n-1} A000041(n-k)*A(k;x)*x, A(0;x) = 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 02 2004
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EXAMPLE
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Table begins 1; 2 1; 3 4 1; 5 10 6 1; ...
For n=4 there are 5 partitions of 4, namely 4, 31, 22, 211, 11111. There are 5 ways to pick 1 of them; 10 ways to partition one of them into 2 ordered parts: 3,1; 1,3; 2,2; 21,1; 1,21; 2,11; 11,2; 111,1; 1,111; 11,11; 6 ways to partition one of them into 3 ordered parts: 2,1,1; 1,2,1; 1,1,2; 11,1,1; 1,11,1; 1,1,11; and one way to partition one of them into 4 ordered parts: 1,1,1,1. So row 4 is 5,10,6,1.
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CROSSREFS
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Cf. A000041, A048574, A055887, A055888.
Sequence in context: A126198 A055888 A094442 this_sequence A154929 A049400 A106382
Adjacent sequences: A060639 A060640 A060641 this_sequence A060643 A060644 A060645
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Apr 16 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 02 2004
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