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 A321388 #12 Sep 08 2022 08:46:23 %S A321388 1,1,1,4,19,144,1443,18295,280918,5069651,105147307,2464296222, %T A321388 64402891501,1856989724951,58560557062508,2004999890781363, %U A321388 74069439021212783,2936703201134924845,124383305232306494864,5605027085651919547476,267759074907470856179460,13516676464234372267564939 %N A321388 Expansion of Product_{k>=1} (1 + x^k)^(k^(k-2)). %C A321388 Weigh transform of A000272. %H A321388 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a> %F A321388 G.f.: exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d+1)*d^(d-1) ) * x^k/k). %F A321388 a(n) ~ n^(n-2) * (1 + exp(-1)/n + (5*exp(-1)/2 + exp(-2))/n^2). - _Vaclav Kotesovec_, Nov 09 2018 %p A321388 a:=series(mul((1+x^k)^(k^(k-2)),k=1..100),x=0,22): seq(coeff(a,x,n),n=0..21); # _Paolo P. Lava_, Apr 02 2019 %t A321388 nmax = 21; CoefficientList[Series[Product[(1 + x^k)^(k^(k - 2)), {k, 1, nmax}], {x, 0, nmax}], x] %t A321388 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d^(d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 21}] %o A321388 (PARI) m=30; x='x+O('x^m); Vec(prod(k=1,m,(1+x^k)^(k^(k-2)))) \\ _G. C. Greubel_, Nov 09 2018 %o A321388 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 + x^k)^(k^(k-2)): k in [1..m]]) )); // _G. C. Greubel_, Nov 09 2018 %Y A321388 Cf. A000272, A261053, A262842, A321386, A321387. %K A321388 nonn %O A321388 0,4 %A A321388 _Ilya Gutkovskiy_, Nov 08 2018