cp's OEIS Frontend

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.

A307648 G.f. A(x) satisfies: 1/(1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

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%I A307648 #6 Apr 20 2019 08:11:49
%S A307648 1,1,-1,-4,-3,-2,7,7,4,-6,14,-11,-4,-47,9,6,161,-93,-33,-269,232,-83,
%T A307648 660,-733,500,-779,1527,-2291,1876,-3892,5598,-3056,7791,-14088,11289,
%U A307648 -17113,28083,-26211,34645,-60715,73180,-80951,111926,-155269,178561,-233709,359679,-403884,454659,-697310,862133
%N A307648 G.f. A(x) satisfies: 1/(1 - x) = A(x)*A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...
%C A307648 Euler transform of A055615.
%F A307648 G.f.: Product_{k>=1} 1/(1 - x^k)^(mu(k)*k).
%F A307648 G.f.: exp(Sum_{k>=1} A046970(k)*x^k/k).
%e A307648 G.f.: A(x) = 1 + x - x^2 - 4*x^3 - 3*x^4 - 2*x^5 + 7*x^6 + 7*x^7 + 4*x^8 - 6*x^9 + 14*x^10 - 11*x^11 - 4*x^12 - 47*x^13 + ...
%t A307648 terms = 50; CoefficientList[Series[Product[1/(1 - x^k)^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]
%t A307648 terms = 50; CoefficientList[Series[Exp[Sum[Sum[MoebiusMu[d] d^2, {d, Divisors[k]}] x^k/k, {k, 1, terms}]], {x, 0, terms}], x]
%t A307648 terms = 50; A[_] = 1; Do[A[x_] = 1/((1 - x) Product[A[x^k]^k, {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
%Y A307648 Cf. A008683, A046970, A055615, A117209, A307649.
%K A307648 sign
%O A307648 0,4
%A A307648 _Ilya Gutkovskiy_, Apr 19 2019