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.

A300277 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} 1/(1 - n*x^n).

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%I A300277 #8 Jun 07 2021 13:22:45
%S A300277 1,2,5,11,24,48,96,184,348,645,1169,2140,3761,6687,11645,20326,34635,
%T A300277 59854,100579,171211,285718,479325,791315,1318955,2156805,3553589,
%U A300277 5783306,9445861,15250215,24759156,39713787,63991400,102197851,163548416,259744930,413761633,653715967
%N A300277 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} 1/(1 - n*x^n).
%C A300277 Moebius transform of A006906.
%H A300277 Vaclav Kotesovec, <a href="/A300277/b300277.txt">Table of n, a(n) for n = 1..6000</a>
%H A300277 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A300277 a(n) = Sum_{d|n} mu(n/d)*A006906(d).
%t A300277 nn = 37; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[1/(1 - n x^n), {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%t A300277 s[n_] := SeriesCoefficient[Product[1/(1 - k x^k), {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] s[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 37}]
%Y A300277 Cf. A000837, A006906, A078374, A085410, A300274, A300275, A300276, A300278.
%K A300277 nonn
%O A300277 1,2
%A A300277 _Ilya Gutkovskiy_, Mar 01 2018