Search: id:A026838
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%I A026838
%S A026838 0,1,1,1,1,2,3,3,4,5,6,7,9,11,14,16,19,23,27,32,38,44,52,61,71,
%T A026838 83,96,111,128,148,170,195,224,256,292,334,380,432,491,557,630,
%U A026838 713,805,908,1024,1152,1295,1455,1632,1829,2048,2291,2560,2859
%N A026838 Number of partitions of n into distinct parts, the greatest being even.
%C A026838 Fine's theorem: a(n) - A026837(n) = 1 if n = k(3k+1)/2, = -1 if n = k(3k-1)/
               2, = 0 otherwise.
%C A026838 Also number of partitions of n into an even number of parts and such 
               that parts of every size from 1 to the largest occur. Example: a(8)=3 
               because we have [3,2,2,1],[2,2,1,1,1,1] and [1,1,1,1,1,1,1,1]. - 
               Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
%D A026838 I. Pak, On Fine's partition theorems, Dyson, Andrews and missed opportunities, 
               Math. Intelligencer, 25 (No. 1, 2003), 10-16.
%F A026838 G.f.=sum(x^(2k)*product(1+x^j, j=1..2k-1), k=1..infinity). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Apr 04 2006
%F A026838 a(2*n)=A118301(2*n), a(2*n-1)=A118302(2*n-1); a(n)=A000009(n)-A026837(n). 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2006
%e A026838 a(8)=3 because we have [8],[6,2] and [4,3,1].
%p A026838 g:=sum(x^(2*k)*product(1+x^j,j=1..2*k-1),k=1..50): gser:=series(g,x=0,
               75): seq(coeff(gser,x,n),n=1..54); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 04 2006
%Y A026838 Cf. A026837.
%Y A026838 Cf. A027187.
%Y A026838 Sequence in context: A039732 A011876 A029036 this_sequence A017864 A029035 
               A153178
%Y A026838 Adjacent sequences: A026835 A026836 A026837 this_sequence A026839 A026840 
               A026841
%K A026838 nonn
%O A026838 1,6
%A A026838 Clark Kimberling (ck6(AT)evansville.edu)

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