A376784 Expansion of 1/sqrt((1 - x^3 - x^5)^2 - 4*x^8).
1, 0, 0, 1, 0, 1, 1, 0, 4, 1, 1, 9, 1, 9, 16, 2, 36, 25, 17, 100, 37, 101, 225, 74, 401, 442, 289, 1226, 820, 1306, 3138, 1737, 5000, 7106, 5161, 15998, 15185, 18901, 44308, 34282, 67861, 110365, 92501, 219609, 259621, 295242, 637570, 620350, 986373, 1694619
Offset: 0
Keywords
Programs
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Mathematica
CoefficientList[Series[1/Sqrt[(1-x^3-x^5)^2-4x^8],{x,0,50}],x] (* Harvey P. Dale, Apr 28 2025 *) -
PARI
my(N=50, x='x+O('x^N)); Vec(1/sqrt((1-x^3-x^5)^2-4*x^8)) -
PARI
a(n) = sum(k=0, n\5, ((n-2*k)%3==0)*binomial((n-2*k)/3, k)^2);
Formula
G.f.: 1/sqrt((1 - x^3 + x^5)^2 - 4*x^5) = 1/sqrt((1 + x^3 - x^5)^2 - 4*x^3).