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 A345878 #8 Jun 28 2021 15:56:48
%S A345878 1,-2,5,-18,70,-282,1179,-5104,22634,-102128,467637,-2168208,10157664,
%T A345878 -48005858,228607728,-1095885048,5284044080,-25609804110,124693451466,
%U A345878 -609641464746,2991742731876,-14731354000792,72761153346680,-360397156557696,1789733084330806,-8909067981051118
%N A345878 G.f. A(x) satisfies: A(x) = x / exp(2 * Sum_{k>=1} A(x^k) / k).
%F A345878 G.f.: x * Product_{n>=1} (1 - x^n)^(2*a(n)).
%F A345878 a(n+1) = -(2/n) * Sum_{k=1..n} ( Sum_{d|k} d * a(d) ) * a(n-k+1).
%p A345878 a:= proc(n) option remember; `if`(n=1, 1, -2*add(a(n-k)*add(
%p A345878 d*a(d), d=numtheory[divisors](k)), k=1..n-1)/(n-1))
%p A345878 end:
%p A345878 seq(a(n), n=1..26); # _Alois P. Heinz_, Jun 28 2021
%t A345878 nmax = 26; A[_] = 0; Do[A[x_] = x/Exp[2 Sum[A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t A345878 a[1] = 1; a[n_] := a[n] = -(2/(n - 1)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 26}]
%Y A345878 Cf. A000151, A005753, A045648, A345883.
%K A345878 sign
%O A345878 1,2
%A A345878 _Ilya Gutkovskiy_, Jun 28 2021