A278297 a(n) = A278296(n) - A238132(n).

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

Offset: 0

Author

Vladimir Reshetnikov, Nov 17 2016

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, q-Polygamma Function, q-Pochhammer Symbol.

Crossrefs

Cf. A278296, A238132.

Programs

Mathematica

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}]

Formula

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.