Search: id:A145740
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%I A145740
%S A145740 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 A145740 16,5,62,24,60,24,10,94,40,91,38,18,144,62,136,57,24,214,88,201,82,30,
%U A145740 308,122,288,117,48,440,180,410,168,74,624,262,578,238,96,874,356,804
%V A145740 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 A145740 -16,5,-62,24,60,-24,10,-94,40,91,-38,18,-144,62,136,-57,24,-214,88,201,
               -82,30,-308,
%X A145740 122,288,-117,48,-440,180,410,-168,74,-624,262,578,-238,96,-874,356,804
%N A145740 McKay-Thompson series of class 20C for the Monster group with a(0) = 
               -2.
%F A145740 Expansion of (eta(q) * eta(q^4) * eta(q^10) / (eta(q^2) * eta(q^5) * 
               eta(q^20)))^2 in powers of q.
%F A145740 G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 5 
               / f(t) where q = exp(2 pi i t).
%F A145740 Expansion of q^(-1) * (psi(-q) / psi(-q^5))^2 in powers of q where psi() 
               is a Ramanujan theta function.
%e A145740 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 A145740 (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 
               (eta(x + A) * eta(x^4 + A) * eta(x^10 + A) / (eta(x^2 + A) * eta(x^5 
               + A) * eta(x^20 + A)))^2, n))}
%Y A145740 A112159(n) = a(n) unless n=0. Convolution square of A145708. -2 * A138522(n) 
               = a(2*n).
%Y A145740 Sequence in context: A134997 A104605 A138516 this_sequence A026513 A106028 
               A105307
%Y A145740 Adjacent sequences: A145737 A145738 A145739 this_sequence A145741 A145742 
               A145743
%K A145740 sign
%O A145740 -1,2
%A A145740 Michael Somos, Oct 17 2008

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