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.

A300276 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n)^n.

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%I A300276 #6 Mar 01 2018 14:54:00
%S A300276 1,1,4,6,15,22,48,75,137,218,384,593,1003,1549,2501,3857,6110,9256,
%T A300276 14408,21675,33081,49422,74483,110135,164116,240955,355027,517553,
%U A300276 755893,1093649,1584518,2277986,3274887,4679619,6682635,9491959,13471238,19030370,26849913,37734570
%N A300276 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n)^n.
%C A300276 Moebius transform of A026007.
%H A300276 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A300276 a(n) = Sum_{d|n} mu(n/d)*A026007(d).
%t A300276 nn = 40; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[(1 + x^n)^n, {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%t A300276 s[n_] := SeriesCoefficient[Product[(1 + x^k)^k, {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] s[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 40}]
%Y A300276 Cf. A000837, A026007, A078374, A300274, A300275, A300277, A300278.
%K A300276 nonn
%O A300276 1,3
%A A300276 _Ilya Gutkovskiy_, Mar 01 2018