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.

A028343 Expansion of Product_{i>=1} (1-x^i)^(1/i); also of exp(- Sum_{n>=1}(d(n)*x^n/n)) where d(n) is the number of divisors of n.

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%I A028343 #14 Nov 25 2016 14:26:14
%S A028343 1,-1,-1,1,-1,41,-131,1499,-4159,10639,100871,4142249,-111459041,
%T A028343 1127459321,1797229589,-185028952109,706529394689,29136228245279,
%U A028343 -547852336663409,7139784702100049,-195178627579232449
%N A028343 Expansion of Product_{i>=1} (1-x^i)^(1/i); also of exp(- Sum_{n>=1}(d(n)*x^n/n)) where d(n) is the number of divisors of n.
%H A028343 G. C. Greubel, <a href="/A028343/b028343.txt">Table of n, a(n) for n = 0..445</a>
%F A028343 E.g.f.: Product_{i>=1} (1-x^i)^(1/i).
%e A028343 G.f. = 1 - x - x^2 + x^3 - x^4 + 41*x^5 - 131*x^6 + 1499*x^7 - 4159*x^8 + ...
%t A028343 nmax = 50; CoefficientList[Series[Product[(1 - x^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x]*Range[0, nmax]! (* _G. C. Greubel_, Nov 24 2016 *)
%t A028343 a[ n_] := If[n < 0, 0, n! SeriesCoefficient[ Exp[ -Sum[DivisorSigma[0, k] x^k/k, {k, n}]], {x, 0, n}]]; (* _Michael Somos_, Nov 25 2016 *)
%K A028343 sign
%O A028343 0,6
%A A028343 _Jeffrey Shallit_