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Search: id:A060850
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| A060850 |
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Sequence formed from antidiagonals of matrix defined by coefficients a[e,m] in Taylor expansion of P=Product[(1-x^n)^-e,{n,+Infinity}] i.e. P==Sum[a[e,m] x^m, {m,0,+Infinity}], e = 1, 2, 3, ... |
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+0
6
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| 1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 9, 10, 5, 1, 5, 14, 22, 20, 7, 1, 6, 20, 40, 51, 36, 11, 1, 7, 27, 65, 105, 108, 65, 15, 1, 8, 35, 98, 190, 252, 221, 110, 22, 1, 9, 44, 140, 315, 506, 574, 429, 185, 30, 1, 10, 54, 192, 490, 918, 1265, 1240, 810, 300, 42, 1, 11, 65, 255
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Table read by antidiagonals: entry (n,k) gives number of partitions of n objects into parts of k kinds. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 28 2006
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FORMULA
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G.f. A(n;x) for n-th row satisfies A(n;x) = Sum_{k=1..n} A000041(k-1)*A(n-k;x)*x^(k-1), A(0;x) = 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 02 2004
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CROSSREFS
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Cf. A067687 (row sums).
Columns: A000041, A000712, A000716, A023003-A023021, A006922. Rows: A000012, A000027, A000096, A006503, A006504.
Sequence in context: A046752 A086350 A140767 this_sequence A038137 A073133 A106179
Adjacent sequences: A060847 A060848 A060849 this_sequence A060851 A060852 A060853
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KEYWORD
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tabl,nonn,easy
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AUTHOR
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Bo T. Ahlander (ahlboa(AT)isk.kth.se), May 03 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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