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 A163920 #11 Jul 17 2023 04:34:22 %S A163920 1,0,12,9,30,0,56,60,126,0,132,126,182,0,420,316,306,0,380,330,798,0, %T A163920 552,888,875,0,1296,630,870,0,992,1536,1914,0,2100,1467,1406,0,2652, %U A163920 2360,1722,0,1892,1518,4860,0,2256,4872,3234,0,4488,2106,2862,0,5060 %N A163920 Expansion of Sum_{k>0} k*(k+1)/2 * x^k / (1 - (-x)^k)^3. %H A163920 Seiichi Manyama, <a href="/A163920/b163920.txt">Table of n, a(n) for n = 1..10000</a> %F A163920 a(4n+2) = 0. %F A163920 a(2n+1) = A034715(2n+1), where A034715 is the Dirichlet convolution of triangular numbers with themselves. %F A163920 a(n) = (n/4) * Sum_{d|n} (-1)^(n+d) * (d+1) * (n/d+1). - _Seiichi Manyama_, Jul 17 2023 %t A163920 CoefficientList[Series[Sum[((k(k+1))/2 x^k)/(1-(-x)^k)^3,{k,100}],{x,0,100}],x] (* _Harvey P. Dale_, May 08 2021 *) %o A163920 (PARI) {a(n) = if( n<1, 0, polcoeff( sum(k=1, n, k*(k+1)/2 * x^k / (1 - (-x)^k)^3, x*O(x^n)), n))} %Y A163920 Cf. A143520 (variant), A034715. %K A163920 nonn %O A163920 1,3 %A A163920 _Paul D. Hanna_, Aug 06 2009