Search: id:A081360
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%I A081360
%S A081360 1,1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,
%T A081360 142,165,192,222,256,296,340,390,448,512,585,668,760,864,982,1113,1260,
%U A081360 1426,1610,1816,2048,2304,2590,2910,3264,3658,4097,4582,5120,5718,6378
%V A081360 1,-1,1,-2,2,-3,4,-5,6,-8,10,-12,15,-18,22,-27,32,-38,46,-54,64,-76,89,
               -104,122,
%W A081360 -142,165,-192,222,-256,296,-340,390,-448,512,-585,668,-760,864,-982,1113,
               -1260,
%X A081360 1426,-1610,1816,-2048,2304,-2590,2910,-3264,3658,-4097,4582,-5120,5718,
               -6378
%N A081360 Expansion of q^(-1/24)(m(1-m)/16)^(1/24) in powers of q, where m=k^2 
               is the parameter and q is the nome for Jacobian elliptic functions.
%C A081360 Number of partitions of n into distinct parts with an even number of 
               odd parts minus partitions of n into distinct parts with an odd number 
               of odd parts. G.f. : product(i=1,oo,1+(-1)^i*x^i) - Jon Perry (perry(AT)globalnet.co.uk), 
               Jun 04 2004
%C A081360 Apart from signs, identical to A000009.
%F A081360 Euler transform of period 4 sequence [ -1, 1, -1, 0, ...].
%F A081360 Given g.f. A(x), B(x)=x* A(x^3)^8 satisfies 0=f(B(x), B(x^2)) where f(u, 
               v)= (u-v^2)* (v-u^2) -(4*u*v* (1-u*v))^2.
%F A081360 G.f. is Fourier series of a weight 0 level 2304 modular form. f(-1/ (2304 
               t)) = f(t) where q = exp(2 pi i t). - Michael Somos Jul 16 2007
%F A081360 G.f.: Product_{k>0} 1/(1+x^(2k-1)).
%F A081360 Expansion of 1/chi(q) in powers of q where chi() is a Ramanujan theta 
               function.
%F A081360 Expansion of q^(-1/24) * eta(q) * eta(q^4) / eta(q^2)^2 in powers of 
               q.
%F A081360 Expansion of q^(-1/24) / f(t) in powers of q=exp(Pi i t) where f() is 
               Weber's function.
%F A081360 G.f. is Fourier series of a weight 0 level 2304 modular form. f(-1/ (2304 
               t)) = f(t) where q = exp(2 pi i t).
%e A081360 q - q^25 + q^49 - 2*q^73 + 2*q^97 - 3*q^121 + 4*q^145 - 5*q^169 + ...
%p A081360 read theta; t1:=series(eta,q,48); t2:= q^(-1/24)*t1*subs(q=q^4,t1)/subs(q=q^2,
               t1)^2; series(t2,q,48); seriestolist(%); - N. J. A. Sloane (njas(AT)research.att.com), 
               Aug 24 2007
%o A081360 (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)/
               eta(x^2+A)^2, n))}
%Y A081360 A000009(n)=(-1)^n a(n). Convolution inverse of A000700.
%Y A081360 Sequence in context: A058703 A034320 A000009 this_sequence A117409 A092833 
               A100926
%Y A081360 Adjacent sequences: A081357 A081358 A081359 this_sequence A081361 A081362 
               A081363
%K A081360 sign
%O A081360 0,4
%A A081360 Michael Somos, Mar 18 2003

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