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.

A281457 Expansion of Product_{k>=1} (1 + x^(7*k-4)).

This page as a plain text file.
%I A281457 #6 Jan 24 2017 09:58:55
%S A281457 1,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,2,0,0,1,1,0,0,
%T A281457 2,0,0,1,1,0,0,3,0,0,2,1,0,0,3,0,0,3,1,0,1,4,0,0,4,1,0,1,4,0,0,5,1,0,
%U A281457 2,5,0,0,7,1,0,3,5,0,0,8,1,0,5,6,0,1
%N A281457 Expansion of Product_{k>=1} (1 + x^(7*k-4)).
%H A281457 Vaclav Kotesovec, <a href="/A281457/b281457.txt">Table of n, a(n) for n = 0..10000</a>
%F A281457 a(n) ~ exp(sqrt(n/21)*Pi) / (2^(10/7)*21^(1/4)*n^(3/4)) * (1 - (3*sqrt(21)/(8*Pi) + 23*Pi/(336*sqrt(21))) / sqrt(n)). - _Vaclav Kotesovec_, Jan 22 2017, extended Jan 24 2017
%t A281457 nmax = 100; CoefficientList[Series[Product[(1 + x^(7*k - 4)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A281457 nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 7] == 3, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
%Y A281457 Cf. A109705, A281245, A281455, A281456, A281458, A280457.
%K A281457 nonn
%O A281457 0,28
%A A281457 _Vaclav Kotesovec_, Jan 22 2017