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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 6, 10, 14, 22, 28, 40, 52, 70, 88, 116, 142, 180, 228, 280, 342, 422, 510, 620, 750, 902, 1084, 1296, 1544, 1834, 2182, 2574, 3042, 3580, 4208, 4920, 5762, 6728, 7838, 9108, 10574, 12240
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refs;
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OFFSET
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0,22
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (2^n - 2*n) * x^(n*(2*n+1)) / (x; x)_{2*n}, where (a; q)_n = Product_{k=0..n-1} (1 - a*q^n) is the q-Pochhammer symbol.
G.f.: ((sqrt(2)-1)*(-sqrt(2); x)_inf - (sqrt(2)+1)*(sqrt(2); x)_inf)/2 + (2*(x; x)_inf * (log(1-x) + psi_x(1)) + (-1; x)_inf * (log(1-x) + psi_x(1 - log(-1)/log(x))))/(4*log(x)), where psi_q(z) is the q-digamma function, and (a; q)_inf = Product_{k>=0} (1 - a*q^n) is the q-Pochhammer symbol (the Euler function), log(-1) = i*Pi.
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MATHEMATICA
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Table[SeriesCoefficient[FunctionExpand[Sum[(2^n - 2 n) x^(n (2 n + 1))/QPochhammer[x, x, 2 n], {n, 0, Sqrt[k/2]}]], {x, 0, k}], {k, 0, 60}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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