Search: id:A026832
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%I A026832
%S A026832 1,0,2,1,2,2,4,4,5,6,8,10,12,14,18,21,24,30,36,42,50,58,68,80,
%T A026832 93,108,126,146,168,194,224,256,294,336,384,439,500,568,646,732,
%U A026832 828,938,1060,1194,1348,1516,1704,1916,2149,2408,2698,3018,3372
%N A026832 Number of partitions of n into distinct parts, the least being odd.
%C A026832 Fine's numbers L(n).
%C A026832 Also number of partitions of n such that if k is the largest part, then 
               k occurs an odd number of times and each of the numbers 1,2,...,k-1 
               occurs at least once. Example: a(7)=4 because we have [3,2,1,1],[2,
               2,2,1],[2,1,1,1,1,1] and [1,1,1,1,1,1,1] - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 29 2006
%D A026832 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. 
               Soc., 1988; p. 56, Eq. (26.28).
%F A026832 G.f.: Sum_{k>=1} ((-1)^(k+1)*(-1+Product_{i>=k} (1+x^i))). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Aug 26 2003
%F A026832 G.f.: Sum_{ k >= 1 } x^(k*(k+1)/2)/((1+x^k)*Product_{i=1..k} (1-x^i) 
               ). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2004
%F A026832 (1 + Sum_{n >= 1} a(n)q^n )*(1 + 2 Sum_{m>=1} (-1)^m*q^(m^2)) = Sum_{n 
               >= 1} (-1)^n*q^((3*n^2+n)/2)/(1+q^n). [Fine]
%F A026832 G.f.=sum(x^(2k-1)*product(1+x^j, j=2k..infinity), k=1..infinity). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006
%e A026832 a(7)=4 because we have [7],[6,1],[4,3] and [4,2,1].
%p A026832 g:=sum(x^(2*k-1)*product(1+x^j,j=2*k..60),k=1..60): gser:=series(g,x=0,
               55); seq(coeff(gser,x^n),n=1..53); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 29 2006
%Y A026832 Cf. A026804, A026805, A026807, A092265, A096661, A097042.
%Y A026832 Sequence in context: A133770 A163373 A117193 this_sequence A089408 A079318 
               A050315
%Y A026832 Adjacent sequences: A026829 A026830 A026831 this_sequence A026833 A026834 
               A026835
%K A026832 nonn,nice
%O A026832 1,3
%A A026832 Clark Kimberling (ck6(AT)evansville.edu)
%E A026832 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 29 2006

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