A285339 - OEIS

%I #13 Nov 10 2017 04:58:06

%S 1,0,0,3,0,0,3,7,0,1,21,11,0,21,54,15,7,96,122,19,74,311,217,44,351,

%T 768,367,209,1227,1663,591,989,3402,3225,1156,3609,8289,5815,3053,

%U 11096,18015,10176,9466,29593,36249,18454,28960,71093,68438,37297,81606

%N Expansion of Product_{k>=0} (1 + x^(4*k+3))^(4*k+3).

%H Seiichi Manyama, <a href="/A285339/b285339.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (-1)^n * A285213(n).

%F a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - _Vaclav Kotesovec_, Nov 10 2017

%Y Product_{k>=0} (1 + x^(m*k+m-1))^(m*k+m-1): A262736 (m=2), A262948 (m=3), this sequence (m=4), A285340 (m=5).

%Y Cf. A285213, A285311.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Apr 17 2017