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A113259 Expansion of psi(x)^5 / psi(x^5) - 25*x^2 * psi(x) * psi(x^5)^3 in powers of x where psi() is a Ramanujan theta function. 1

%I

%S 1,5,-15,-10,25,5,30,-30,-55,35,-15,60,-50,-60,90,-10,105,-80,-105,

%T 100,25,60,-180,-110,110,5,180,-100,-150,150,30,160,-215,-120,240,-30,

%U 175,-180,-300,120,-55,210,-180,-210,300,35,330,-230,-210,215,-15,160,-300,-260,300,60,330,-200,-450

%N Expansion of psi(x)^5 / psi(x^5) - 25*x^2 * psi(x) * psi(x^5)^3 in powers of x where psi() is a Ramanujan theta function.

%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

%D B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 249 Entry 8(iv).

%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>

%F G.f.: 1 + 5*( Sum_{k>0} (k*x^k / (1 + x^k)) * Kronecker(5, k) ).

%F a(n) = 5 * A113260(n) if n>0.

%e G.f. = 1 + 5*x - 15*x^2 - 10*x^3 + 25*x^4 + 5*x^5 + 30*x^6 - 30*x^7 - 55*x^8 + ...

%t a[ n_] := If[ n < 1, Boole[n == 0], -5 DivisorSum[ n, # KroneckerSymbol[ 5, #] (-1)^(n/#) &]]; (* _Michael Somos_, Sep 07 2018 *)

%o (PARI) {a(n) = if( n<1, n==0, -5 * sumdiv(n, d, d * kronecker(5, d) * (-1)^(n/d)))};

%Y Cf. A113260.

%K sign

%O 0,2

%A _Michael Somos_, Oct 20 2005

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)