A292526 Expansion of x^1 * (1-x^1) / (1+x^1)^2 - x^4 * (1-x^3) * (1+x^3)^2 + x^9 * (1-x^5) / (1+x^5)^2 - ... in powers of x.
0, 1, -3, 5, -8, 9, -11, 16, -15, 18, -24, 21, -23, 32, -30, 29, -41, 33, -35, 53, -39, 41, -56, 48, -54, 65, -51, 53, -72, 66, -64, 80, -63, 65, -102, 69, -72, 103, -75, 90, -104, 81, -83, 117, -111, 89, -120, 96, -95, 146, -99, 112, -143, 105, -126, 144
Offset: 0
Keywords
Examples
G.f. = x - 3*x^2 + 5*x^3 - 8*x^4 + 9*x^5 - 11*x^6 + 16*x^7 - 15*x^8 + 18*x^9 + ...
References
- G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See p. 278, Equ. (12.4.23).
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
Programs
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Maple
seq(coeff(series(add(-(-1)^k*x^(k^2)*(1-x^(2*k-1))/(1+x^(2*k-1))^2,k=1..n), x,n+1),x,n),n=0..60); # Muniru A Asiru, Jul 29 2018
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Mathematica
a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ -(-1)^k x^k^2 (1 - x^(2 k - 1)) / (1 + x^(2 k - 1))^2, {k, Sqrt@n}], {x, 0, n}]]; -
PARI
{a(n) = if( n<0, 0, polcoeff( sum(k=1, sqrtint(n), -(-1)^k * x^(k^2) * (1 - x^(2*k-1) + x * O(x^(n-k^2))) / (1 + x^(2*k-1))^2), n))};
Comments