%I A138516
%S A138516 1,2,1,2,2,2,1,0,4,2,5,2,0,8,2,8,3,2,14,6,14,6,4,24,12,24,11,4,40,16,38,
%T A138516 16,5,62,24,60,24,10,94,40,91,38,18,144,62,136,57,24,214,88,201,82,30,
%U A138516 308,122,288,117,48,440,180,410,168,74,624,262,578,238,96,874,356,804
%V A138516 1,2,1,2,2,-2,-1,0,-4,-2,5,2,0,8,2,-8,-3,-2,-14,-6,14,6,4,24,12,-24,-11,
               -4,-40,-16,38,
%W A138516 16,5,62,24,-60,-24,-10,-94,-40,91,38,18,144,62,-136,-57,-24,-214,-88,
               201,82,30,308,
%X A138516 122,-288,-117,-48,-440,-180,410,168,74,624,262,-578,-238,-96,-874,-356,
               804
%N A138516 McKay-Thompson series of class 10E for the Monster group with a(0) = 
               2.
%H A138516 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%F A138516 Expansion of q^(-1) * (psi(q) / psi(q^5))^2 in powers of q where psi() 
               is a Ramanujan theta function.
%F A138516 Expansion of ((eta(q^2) / eta(q^10))^2 * eta(q^5) / eta(q))^2 in powers 
               of q.
%F A138516 Euler transform of period 10 sequence [ 2, -2, 2, -2, 0, -2, 2, -2, 2, 
               0, ...].
%F A138516 G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u^2 - v) * (v 
               - 1) - 4 * v * (u - 1).
%F A138516 G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u 
               * (u - 1) * (u - 5) * v * (v - 1) * (v - 5).
%F A138516 G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 5 
               g(t) where q = exp(2 pi i t) and g() is g.f. for A138517.
%F A138516 G.f.: (1/x) * (Product_{k>0} P(5,x^k) * P(10,x^k)^2)^(-2) where P(n,x) 
               is the nth cyclotomic polynomial.
%e A138516 1/q + 2 + q + 2*q^2 + 2*q^3 - 2*q^4 - q^5 - 4*q^7 - 2*q^8 + 5*q^9 + ...
%o A138516 (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 
               ( (eta(x^2 + A) / eta(x^10 + A))^2 * eta(x^5 + A) / eta(x + A))^2, 
               n))}
%Y A138516 A058101(n) = a(n) unless n=0. Convolution inverse of A138519. Convolution 
               square of A138532.
%Y A138516 Cf. A132980. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 
               2008]
%Y A138516 Sequence in context: A166548 A134997 A104605 this_sequence A145740 A026513 
               A106028
%Y A138516 Adjacent sequences: A138513 A138514 A138515 this_sequence A138517 A138518 
               A138519
%K A138516 sign
%O A138516 -1,2
%A A138516 Michael Somos, Mar 23 2008