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Search: id:A134737
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| A134737 |
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Number of partitions of the n-th partition number into positive parts not greater than n. |
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+0
3
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| 1, 2, 3, 6, 13, 44, 131, 638, 3060, 22367, 167672, 2127747, 26391031, 537973241, 12274276512, 429819314124, 16928838590640, 1068323095351171, 75345432929798690, 8339062208354516217, 1083103359596125913021
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Eric Weisstein's World of Mathematics, Partition
Eric Weisstein's World of Mathematics, Partition Function P
Index entries for sequences related to partitions
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FORMULA
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a(n) = A026820(A026820(n,n),n) = A026820(A000041(n),n).
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MAPLE
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with (numtheory): P:= proc(n) local d, j; P(n):= `if`(n=0, 1, add (add (d, d=divisors(j)) *P(n-j), j=1..n)/n) end: b:= proc(n, i) if n<0 then 0 elif n=0 then 1 elif i=0 then 0 else b(n, i):= b(n, i-1) +b(n-i, i) fi end: a:= n-> b(P(n), n): seq (a(n), n=1..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 17 2009]
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`IntegerPartitions`"] (* then *) a[n_] := Length@ IntegerPartitions[ PartitionsP[n], n] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 11 2007 *)
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CROSSREFS
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Adjacent sequences: A134734 A134735 A134736 this_sequence A134738 A134739 A134740
Sequence in context: A137273 A135967 A146000 this_sequence A030733 A122839 A121556
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 07 2007
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 17 2009
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