This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A278297 #9 Feb 16 2025 08:33:37
%S A278297 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,
%T A278297 70,88,116,142,180,228,280,342,422,510,620,750,902,1084,1296,1544,
%U A278297 1834,2182,2574,3042,3580,4208,4920,5762,6728,7838,9108,10574,12240
%N A278297 a(n) = A278296(n) - A238132(n).
%H A278297 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PolygammaFunction.html">q-Polygamma Function</a>, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278297 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.
%F A278297 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.
%t A278297 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}]
%Y A278297 Cf. A278296, A238132.
%K A278297 nonn
%O A278297 0,22
%A A278297 _Vladimir Reshetnikov_, Nov 17 2016