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 A320942 #6 Apr 02 2019 05:52:16 %S A320942 2,6,10,20,26,54,66,120,164,262,346,572,730,1110,1506,2182,2866,4156, %T A320942 5402,7612,9978,13638,17730,24200,31092,41558,53572,70692,90250, %U A320942 118406,150146,194794,246610,316678,398730,509560,637594,808342,1009186,1270984,1578530,1978758,2447066 %N A320942 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j))/(1 - x^(k*j))). %C A320942 Inverse Möbius transform of A015128. %H A320942 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a> %F A320942 G.f.: Sum_{k>=1} A015128(k)*x^k/(1 - x^k). %F A320942 G.f.: Sum_{k>=1} (1/theta_4(x^k) - 1), where theta_4() is the Jacobi theta function. %F A320942 a(n) = Sum_{d|n} A015128(d). %p A320942 a:=series(add(-1+mul((1+x^(k*j))/(1-x^(k*j)),j=1..100),k=1..100),x=0,44): seq(coeff(a,x,n),n=1..43); # _Paolo P. Lava_, Apr 02 2019 %t A320942 nmax = 43; Rest[CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j))/(1 - x^(k j)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]] %t A320942 nmax = 43; Rest[CoefficientList[Series[Sum[1/EllipticTheta[4, 0, x^k] - 1, {k, 1, nmax}], {x, 0, nmax}], x]] %t A320942 Table[Sum[Sum[PartitionsP[d - k] PartitionsQ[k], {k, 0, d}], {d, Divisors[n]}], {n, 43}] %Y A320942 Cf. A015128, A047966, A047968, A300274. %K A320942 nonn %O A320942 1,1 %A A320942 _Ilya Gutkovskiy_, Oct 24 2018