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.

A308060 G.f. A(x) satisfies: A(x) = x * exp(Sum_{i>=1} Sum_{j>=1} (-1)^(j+1)*A(x^(i*j))/j).

This page as a plain text file.
%I A308060 #33 Nov 05 2021 06:54:54
%S A308060 1,1,2,5,11,26,65,161,412,1074,2841,7599,20582,56202,154760,429052,
%T A308060 1196802,3356107,9456737,26760173,76017365,216693521,619663800,
%U A308060 1777141141,5110235884,14730604451,42557910762,123210505445,357403386959,1038616488923,3023329186466,8814593734152
%N A308060 G.f. A(x) satisfies: A(x) = x * exp(Sum_{i>=1} Sum_{j>=1} (-1)^(j+1)*A(x^(i*j))/j).
%H A308060 Vaclav Kotesovec, <a href="/A308060/b308060.txt">Table of n, a(n) for n = 1..500</a>
%F A308060 G.f.: x * Product_{i>=1, j>=1} (1 + x^(i*j))^a(j).
%F A308060 a(n) ~ c * d^n / n^(3/2), where d = 3.05850813076802274498884492525... and c = 0.46090575889706771724968759... - _Vaclav Kotesovec_, Nov 05 2021
%t A308060 terms = 32; A[_] = 0; Do[A[x_] = x Exp[Sum[Sum[(-1)^(j + 1) A[x^(i j)]/j, {j, 1, terms}], {i, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
%t A308060 a[n_] := a[n] = SeriesCoefficient[x Product[Product[(1 + x^(i j))^a[j], {j, 1, n - 1}], {i, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 32}]
%Y A308060 Cf. A004111, A179467.
%K A308060 nonn
%O A308060 1,3
%A A308060 _Ilya Gutkovskiy_, May 11 2019