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.

A278401 G.f.: Re(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

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%I A278401 #13 Feb 16 2025 08:33:37
%S A278401 1,-1,-2,-1,-1,-1,-1,1,2,2,2,4,5,5,5,6,7,5,3,4,3,0,-2,-3,-5,-10,-14,
%T A278401 -16,-18,-23,-28,-28,-29,-35,-38,-37,-37,-39,-39,-35,-30,-29,-26,-15,
%U A278401 -5,0,10,26,41,51,64,85,105,119,135,160,183,196,212,236,255,265
%N A278401 G.f.: Re(2/(i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
%C A278401 The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).
%H A278401 Seiichi Manyama, <a href="/A278401/b278401.txt">Table of n, a(n) for n = 0..1000</a>
%H A278401 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278401 2/(i; x)_inf is the g.f. for a(n) + i*A278402(n).
%F A278401 G.f.: Sum_{n >= 0} (-1)^n*x^(2*n)*(1 - x - x^(2*n+1))/Product_{k = 1..2*n+1} (1 - x^k). - _Peter Bala_, Feb 08 2021
%p A278401 with(gfun): series( add( (-1)^n*x^(2*n)*(1 - x - x^(2*n+1))/mul(1 - x^k, k = 1..2*n+1), n = 0..50), x, 101): seriestolist(%); # _Peter Bala_, Feb 08 2021
%t A278401 Re[(2/QPochhammer[I, x] + O[x]^70)[[3]]]
%Y A278401 Cf. A278399, A278400, A278402.
%K A278401 sign,easy
%O A278401 0,3
%A A278401 _Vladimir Reshetnikov_, Nov 20 2016