A278401 - OEIS

%I #12 Feb 09 2021 10:37:44

%S 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 -16,-18,-23,-28,-28,-29,-35,-38,-37,-37,-39,-39,-35,-30,-29,-26,-15,

%U -5,0,10,26,41,51,64,85,105,119,135,160,183,196,212,236,255,265

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

%C The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).

%H Seiichi Manyama, <a href="/A278401/b278401.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

%F 2/(i; x)_inf is the g.f. for a(n) + i*A278402(n).

%F 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 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 Re[(2/QPochhammer[I, x] + O[x]^70)[[3]]]

%Y Cf. A278399, A278400, A278402.

%K sign,easy

%O 0,3

%A _Vladimir Reshetnikov_, Nov 20 2016