Search: id:A027193
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%I A027193
%S A027193 0,1,1,2,2,4,5,8,10,16,20,29,37,52,66,90,113,151,190,248,310,
%T A027193 400,497,632,782,985,1212,1512,1851,2291,2793,3431,4163,5084,
%U A027193 6142,7456,8972,10836,12989,15613,18646,22316,26561,31659,37556
%N A027193 Number of partitions of n into an even number of parts, the least being 
               1; also, a(n+1) = number of partitions of n into an odd number of 
               parts; also, partitions of n+1 in which greatest part is odd.
%C A027193 Also number of partitions of n such that the largest part is even and 
               occurs only once. Example: a(6)=4 because we have [6],[4,2],[4,1,
               1] and [2,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 05 2006
%D A027193 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. 
               Soc., 1988; p. 39, Example 7.
%H A027193 T. D. Noe, <a href="b027193.txt">Table of n, a(n) for n = 1..1000</a>
%F A027193 a(n+1)=(A000041(n)-(-1)^n*A000700(n))/2.
%F A027193 For g.f. see under A027187.
%F A027193 G.f.=sum(x^(2k)/product(1-x^j,j=1..2k-1),k=1..infinity). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Apr 05 2006
%F A027193 a(2*n)=A000701(2*n), a(2*n-1)=A046682(2*n-1); a(n)=A000041(n)-A027187(n). 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2006
%e A027193 a(6)=4 because we have [5,1],[3,1,1,1],[2,2,1,1] and [1,1,1,1,1,1].
%p A027193 g:=sum(x^(2*k)/product(1-x^j,j=1..2*k-1),k=1..40): gser:=series(g,x=0,
               50): seq(coeff(gser,x,n),n=1..45); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 05 2006
%Y A027193 Cf. A027187, A000701, A046682.
%Y A027193 Cf. A026837.
%Y A027193 Sequence in context: A036002 A104504 A027337 this_sequence A126796 A157162 
               A109434
%Y A027193 Adjacent sequences: A027190 A027191 A027192 this_sequence A027194 A027195 
               A027196
%K A027193 nonn
%O A027193 1,4
%A A027193 Clark Kimberling (ck6(AT)evansville.edu)

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