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.

A307241 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*d(k+1)*a(n-k), where d() is the number of divisors (A000005).

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%I A307241 #6 Mar 30 2019 08:39:18
%S A307241 1,2,2,3,6,12,23,42,75,135,248,460,849,1554,2837,5192,9527,17490,
%T A307241 32083,58809,107781,197578,362280,664320,1218069,2233202,4094289,
%U A307241 7506602,13763219,25234674,46266927,84828138,155528132,285154061,522819002,958568628,1757496665,3222295912
%N A307241 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*d(k+1)*a(n-k), where d() is the number of divisors (A000005).
%F A307241 G.f.: -x / Sum_{k>=1} (-x)^k/(1 - (-x)^k).
%F A307241 G.f.: 1 / (d/dx) log(Product_{k>=1} (1 - (-x)^k)^(1/k)).
%t A307241 a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) DivisorSigma[0, k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 37}]
%t A307241 nmax = 37; CoefficientList[Series[-x/Sum[(-x)^k/(1 - (-x)^k), {k, 1, nmax + 1}], {x, 0, nmax}], x]
%t A307241 nmax = 37; CoefficientList[Series[1/D[Log[Product[(1 - (-x)^k)^(1/k), {k, 1, nmax + 1}]], x], {x, 0, nmax}], x]
%Y A307241 Cf. A000005, A002039, A129921, A307242.
%K A307241 nonn
%O A307241 0,2
%A A307241 _Ilya Gutkovskiy_, Mar 30 2019