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Search: id:A079308
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| A079308 |
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For a partition P of a positive integer, let f(P) be the product of k+1, over all parts k in P. Let a(n,r) be the sum of f(P) over all partitions P of n with smallest part r. Sequence gives table of a(n,r) for 1 <= r <= n, in the order a(1,1); a(2,1), a(2,2); a(3,1), a(3,2), a(3,3); ... |
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| 2, 4, 3, 14, 0, 4, 36, 9, 0, 5, 100, 12, 0, 0, 6, 236, 42, 16, 0, 0, 7, 602, 54, 20, 0, 0, 0, 8, 1368, 195, 24, 25, 0, 0, 0, 9, 3242, 246, 92, 30, 0, 0, 0, 0, 10, 7240, 759, 112, 35, 36, 0, 0, 0, 0, 11, 16386, 1134, 232, 40, 42, 0, 0, 0, 0, 0, 12, 35692, 2859, 528, 170, 48, 49, 0
(list; table; graph; listen)
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OFFSET
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0,1
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EXAMPLE
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The partitions with minimal part 3 begin 3, 3+3, 4+3, 5+3, 6+3, 3+3+3, ... which yield the following values of f: 4, 16, 20, 24, 28, 64, ... therefore the 3rd column of our table begins 4,0,0,16,20,24,(28+64)=92,...
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MATHEMATICA
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a[n_, r_] := Which[r>n, 0, r==n, n+1, True, a[n, r]=(r+1)Sum[a[n-r, s], {s, r, n-r}]]; Flatten[Table[a[n, r], {n, 1, 12}, {r, 1, n}]]
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CROSSREFS
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Cf. A074139, A074141.
Adjacent sequences: A079305 A079306 A079307 this_sequence A079309 A079310 A079311
Sequence in context: A114883 A125091 A091861 this_sequence A115399 A109429 A114894
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Alford Arnold (Arnold1940(AT)AOL.com), Feb 09 2003
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Feb 11 2003
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