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A026007
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Expansion of prod(m>=1, (1+q^m)^m ); 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, 4685731, 6682699, 9501979, 13471239, 19044780, 26850921, 37756561, 52955699
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OFFSET
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0,3
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COMMENTS
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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,...). - Gary W. Adamson, Jun 13 2009
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LINKS
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Table of n, a(n) for n=0..41.
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FORMULA
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a(n) = 1/n*Sum_{k=1..n} A078306(k)*a(n-k). - Vladeta Jovovic, Nov 22 2002
G.f. Product_{m=1}^{infinity} (1+x^m)^m. Weighout transform of natural numbers (A000027). Euler transform of A026741. - Franklin T. Adams-Watters, Mar 16 2006
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EXAMPLE
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For n = 4, we have 8 partitions
01: [4]
02: [4']
03: [4'']
04: [4''']
05: [3, 1]
06: [3', 1]
07: [3'', 1]
08: [2, 2']
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PROG
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(PARI)
N=66; q='q+O('q^N);
gf= prod(n=1, N, (1+q^n)^n );
Vec(gf)
/* Joerg Arndt, Oct 06 2012 */
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CROSSREFS
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Cf. A000009, A000219, A000027, A026741.
Cf. A000219 [From Gary W. Adamson, 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
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nonn,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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