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FORMULA
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G.f.: hypergeometric3F2([1/3, 5/6, 7/6], [1, 4/3], 432*z).
E.g.f.: hypergeometric3F3([1/3, 5/6, 7/6], [1, 1, 4/3], 432*z).
a(n) = Integral_{x=0..432} x^n*W(x) dx, n>=0, where W(x) = sqrt(3)/(12*Pi*x^(2/3)) - gamma(2/3)*gamma(5/6)*sqrt(3)*hypergeometric3F2([1/2, 5/6, 5/6], [2/3, 3/2], x/432)/(432*Pi^(5/2)*x^(1/6)) + x^(1/6)*hypergeometric3F2([5/6, 7/6, 7/6], [4/3, 11/6], x/432)/(12960*sqrt(Pi)*gamma(2/3)*gamma(5/6)). W(x) is positive on x = [0, 432], it diverges at x=0, and monotonically decreases for x>0. It appears that at x=432, W(x) tends to a constant value close to 0.0007368284. This integral representation as the n-th power moment of the positive function W(x) on the interval [0, 432] is unique, as W(x) is the solution of the Hausdorff moment problem.
The shape of W(x) in the above integral representation of a(n) resembles very much the shape of the corresponding W(x) in A113424.
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