Search: id:A002318
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%I A002318 M2736 N1098
%S A002318 1,3,8,19,42,88,176,339,633,1150,2040,3544,6042,10128,16720,27219,43746,
%T A002318 69483,109160,169758,261504,399272,604560,908248,1354427,2005710,
%U A002318 2950544,4313232,6267642,9055856,13013440,18603603,26463168,37464230
%N A002318 Expansion of (1/theta_4(q)^2 -1)/4 in powers of q.
%D A002318 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002318 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002318 J. W. L. Glaisher, "On the Coefficients in the q-series for pi/2K and 
               2G/pi", Quart J. Pure and Applied Math., 21 (1885), 60-76.
%F A002318 Expansion of (eta(q^2)^2/eta(q)^4 -1)/4 in powers of q.
%p A002318 seq(coeff(convert(series(mul(( 1 - x^k )^(-(2+(k mod 2)*2)),k=1..100),
               x,100),polynom),x,i)/4,i=1..50); (Pab Ter)
%o A002318 (PARI) a(n)=local(A); if(n<1, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2/eta(x+A)^4,
               n)/4) /* Michael Somos Feb 09 2006 */
%Y A002318 Equals (1/4) * A001934(n).
%Y A002318 Sequence in context: A089924 A072916 A074839 this_sequence A095681 A079583 
               A099050
%Y A002318 Adjacent sequences: A002315 A002316 A002317 this_sequence A002319 A002320 
               A002321
%K A002318 nonn
%O A002318 1,2
%A A002318 N. J. A. Sloane (njas(AT)research.att.com).
%E A002318 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 18 2005

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