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A260675 Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions.

%I A260675 #12 Feb 16 2025 08:33:26
%S A260675 1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,2,0,2,0,0,1,2,0,0,0,0,0,2,0,0,1,0,0,0,
%T A260675 0,2,0,0,0,0,0,0,1,0,0,2,0,0,0,0,0,0,0,0,0,0,1,2,0,0,2,0,2,0,0,0,2,0,
%U A260675 0,0,0,2,3,0,0,0,0,0,0,0,2,0,0,0,0,0,0
%N A260675 Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions.
%C A260675 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A260675 G. C. Greubel, <a href="/A260675/b260675.txt">Table of n, a(n) for n = 0..2500</a>
%H A260675 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A260675 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A260675 Expansion of q^(-1/4) * eta(q^4)^2 * eta(q^30)^5 / (eta(q^2) * eta(q^15)^2 * eta(q^60)^2) in powers of q.
%F A260675 Euler transform of a period 60 sequence.
%F A260675 2 * a(n) = A260671(4*n + 1).
%e A260675 G.f. = 1 + x^2 + x^6 + x^12 + 2*x^15 + 2*x^17 + x^20 + 2*x^21 + 2*x^27 + ...
%e A260675 G.f. = q + q^9 + q^25 + q^49 + 2*q^61 + 2*q^69 + q^81 + 2*q^85 + 2*q^109 + ...
%t A260675 a[ n_] := SeriesCoefficient[ (1/2) x^(-1/4) EllipticTheta[ 2, 0, x] EllipticTheta[ 3, 0, x^15], {x, 0, n}];
%o A260675 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^30 + A)^5 / (eta(x^2 + A) * eta(x^15 + A)^2 * eta(x^60 + A)^2), n))};
%Y A260675 Cf. A260671.
%K A260675 nonn
%O A260675 0,16
%A A260675 _Michael Somos_, Nov 14 2015