%I A002300 M0093 N0029
%S A002300 1,2,1,2,1,2,2,3,4,1,5,3,6,8,3,4,8,3,0,2,8,4,4,13,9,5,18,2,2,8,3,10,0,
               4,
%T A002300 2,19,14,7,8,0,20,4,1,8,2,15,7,8,26,10,26,18,10,2,10,28,29,18,20,15,6,
               8,
%U A002300 8,8,2,19,1,0,8,6,28,26,6,23,1,4,12,25,36,14,8,0,18,20,21,12,3,9,0,16,
               48
%V A002300 1,-2,-1,2,1,2,-2,-3,4,1,-5,-3,-6,8,3,4,8,-3,0,-2,-8,-4,-4,-13,9,5,18,
               -2,-2,-8,-3,10,0,-4,
%W A002300 2,19,-14,7,-8,0,-20,-4,-1,8,-2,-15,-7,8,26,-10,26,18,10,-2,10,-28,-29,
               18,-20,-15,6,-8,
%X A002300 8,-8,2,19,-1,0,-8,-6,28,-26,-6,23,-1,4,12,25,-36,-14,8,0,18,20,21,-12,
               -3,-9,0,-16,-48
%N A002300 Coefficients in the expansion of B^2*C^3 in Watson's notation of page 
               118.
%C A002300 Although Watson says these are the coefficients theta_n defined on page 
               128, it appears that this is a mistake, and they are really the coefficients 
               theta'_n. The true theta_n are given in A160528.
%C A002300 Watson's main reason for computing this sequence was to study values 
               of n such that partition(49n+47) == 0 mod 343 (cf. A160553).
%D A002300 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002300 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002300 Watson, G. N.; Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine 
               Angew. Math. (Crelle), 179 (1938), 97-128. See p. 128.
%H A002300 N. J. A. Sloane, <a href="b002300.txt">Table of n, a(n) for n = 0..199</
               a>
%H A002300 GDZ, <a href="http://gdz.sub.uni-goettingen.de/no_cache/dms/load/toc/
               ?IDDOC=238618">Digitized volumes of Crelle</a> [Added by njas, Nov 
               13, 2009]
%F A002300 See Maple code for formula.
%e A002300 x^23-2*x^47-x^71+2*x^95+x^119+2*x^143-2*x^167-3*x^191+4*x^215+x^239-...
%p A002300 M1:=2400:
%p A002300 fm:=mul(1-x^n,n=1..M1):
%p A002300 B:=x*subs(x=x^24,fm):
%p A002300 C:=x^7*subs(x=x^168,fm):
%p A002300 t1:=B^2*C^3;
%p A002300 t2:=series(t1,x,M1);
%p A002300 t3:=subs(x=y^(1/24),t2/x^23);
%p A002300 t4:=series(t3,y,M1/24);
%p A002300 t5:=seriestolist(t4); # A002300
%Y A002300 Cf. A160553.
%Y A002300 Sequence in context: A161054 A161258 A161283 this_sequence A049099 A143179 
               A089610
%Y A002300 Adjacent sequences: A002297 A002298 A002299 this_sequence A002301 A002302 
               A002303
%K A002300 sign,easy,new
%O A002300 0,2
%A A002300 N. J. A. Sloane (njas(AT)research.att.com).
%E A002300 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Nov 14 2009