Search: id:A001934
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%I A001934 M3443 N1397
%S A001934 1,4,12,32,76,168,352,704,1356,2532,4600,8160,14176,24168,40512,66880,
%T A001934 108876,174984,277932,436640,679032,1046016,1597088,2418240,3632992,
%U A001934 5417708,8022840,11802176,17252928,25070568,36223424,52053760,74414412
%N A001934 Expansion of 1/theta_4(q)^2 in powers of q.
%C A001934 Euler transform of period 2 sequence [4,2,...].
%D A001934 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001934 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001934 A. Cayley, A memoir on the transformation of elliptic functions, Collected 
               Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, 
               Vol. 9, p. 128.
%F A001934 G.f.: Product ( 1 - x^k )^{-c(k)}, c(k) = 4, 2, 4, 2, 4, 2, ....
%F A001934 G.f. prod{i=1, oo, (1+x^i)^2}/prod{i=1, oo, (1-x^i)^2} - Jon Perry (perry(AT)globalnet.co.uk), 
               Apr 04 2004
%F A001934 Expansion of eta(q^2)^2/eta(q)^4 in powers of q.
%o A001934 (PARI) y=prod(i=1,20,(1+x^i)^2)/prod(i=1,20,(1-x^i)^2); for(i=0,20,print1(",
               "polcoeff(y,i)))
%o A001934 (PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2/eta(x+A)^4,
               n)) /* Michael Somos Feb 09 2006 */
%Y A001934 Apart from signs, same as A004403.
%Y A001934 Equals 4 * A002318(n), n>0.
%Y A001934 Sequence in context: A133212 A127811 A138517 this_sequence A004403 A084566 
               A079769
%Y A001934 Adjacent sequences: A001931 A001932 A001933 this_sequence A001935 A001936 
               A001937
%K A001934 nonn,easy
%O A001934 0,2
%A A001934 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A001934 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 08 2000
%E A001934 Edited by N. J. A. Sloane (njas(AT)research.att.com) May 13 2008 to remove 
               an incorrect g.f.

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