cp's OEIS Frontend

A278399 G.f.: Re((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).

%I A278399 #17 Feb 16 2025 08:33:37
%S A278399 1,-1,-1,-2,-2,-3,-2,-3,-2,-2,0,0,3,4,8,9,14,16,22,24,30,32,39,40,46,
%T A278399 46,51,48,52,46,46,36,32,16,8,-15,-30,-60,-82,-122,-151,-200,-238,
%U A278399 -296,-342,-412,-464,-542,-602,-686,-750,-841,-904,-996,-1058,-1146,-1198
%N A278399 G.f.: Re((i; x)_inf), where (a; q)_inf is the q-Pochhammer symbol, i = sqrt(-1).
%C A278399 The q-Pochhammer symbol (a; q)_inf = Product_{k>=0} (1 - a*q^k).
%H A278399 Seiichi Manyama, <a href="/A278399/b278399.txt">Table of n, a(n) for n = 0..10000</a>
%H A278399 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.
%F A278399 (i; x)_inf is the g.f. for a(n) + i*A278400(n).
%F A278399 G.f.: Sum_{n >= 0} (-1)^n^x^(n*(2*n-1))/Product_{k = 1..2*n} 1 - x^k. - _Peter Bala_, Feb 04 2021
%p A278399 G := add((-1)^n*x^(n*(2*n-1))/mul(1 - x^k, k = 1..2*n), n = 0..7):
%p A278399 S := series(G, x, 101):
%p A278399 seq(coeff(S, x, j), j = 0..100); # Peter Bala, Feb 04 2021
%t A278399 Re[(QPochhammer[I, x] + O[x]^60)[[3]]]
%Y A278399 Cf. A278400, A278401, A278402, A278420, A292042, A292043.
%K A278399 sign,easy
%O A278399 0,4
%A A278399 _Vladimir Reshetnikov_, Nov 20 2016