Search: id:A026007
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%I A026007
%S A026007 1,1,2,5,8,16,28,49,83,142,235,385,627,1004,1599,2521,3940,
%T A026007 6111,9421,14409,21916,33134,49808,74484,110837,164132,
%U A026007 241960,355169,519158,755894,1096411,1584519,2281926,3275276
%N A026007 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.
%C A026007 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: 
               (Start)
%C A026007 Equals A000219: (1, 1, 3, 6, 13, 24, 48, 86,...) convolved with the aerated
%C A026007 version of the latter: (1, 0, 1, 0, 3, 0, 6, 0, 13,...). (End)
%F A026007 a(n) = 1/n*Sum_{k=1..n} A078306(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 22 2002
%F A026007 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
%e A026007 For n = 4, we have 8 partitions [4], [4'], [4''], [4'''], [3,1], [3',
               1], [3'',1] and [2,2'].
%Y A026007 Cf. A000009, A000219, A000027, A026741.
%Y A026007 A000219 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
%Y A026007 Sequence in context: A096541 A137685 A093065 this_sequence A032233 A026530 
               A032254
%Y A026007 Adjacent sequences: A026004 A026005 A026006 this_sequence A026008 A026009 
               A026010
%K A026007 nonn
%O A026007 0,3
%A A026007 N. J. A. Sloane (njas(AT)research.att.com).

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