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A026007
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Expansion of Product(1+q^m)^m; m=1..inf; number of partitions of n into distinct parts, where n different parts of size n are available.
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3
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1, 1, 2, 5, 8, 16, 28, 49, 83, 142, 235, 385, 627, 1004, 1599, 2521, 3940, 6111, 9421, 14409, 21916, 33134, 49808, 74484, 110837, 164132, 241960, 355169, 519158, 755894, 1096411, 1584519, 2281926, 3275276
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: (Start)
Equals A000219: (1, 1, 3, 6, 13, 24, 48, 86,...) convolved with the aerated
version of the latter: (1, 0, 1, 0, 3, 0, 6, 0, 13,...). (End)
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FORMULA
| a(n) = 1/n*Sum_{k=1..n} A078306(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 22 2002
G.f. Product_{m=1}^{infinity} (1+x^m)^m. Weighout transform of natural numbers (A000027). Euler transform of A026741. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 16 2006
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EXAMPLE
| For n = 4, we have 8 partitions [4], [4'], [4''], [4'''], [3,1], [3',1], [3'',1] and [2,2'].
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CROSSREFS
| Cf. A000009, A000219, A000027, A026741.
A000219 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
Sequence in context: A137685 A169826 A093065 * A032233 A026530 A032254
Adjacent sequences: A026004 A026005 A026006 * A026008 A026009 A026010
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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