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A207571 G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(3*k-1) - 1).

%I A207571 #15 Feb 07 2020 13:37:27
%S A207571 1,2,11,105,1390,23520,484247,11742927,327711230,10343198878,
%T A207571 364237027076,14156867852699,601927703437645,27790427952836499,
%U A207571 1384496764982434033,74027620787319243688,4228343290201028904807,256946673653717460509502,16551666142815138743519611
%N A207571 G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(3*k-1) - 1).
%C A207571 Compare g.f. to: Sum_{n>=0} Product_{k=1..n} ((1+x)^k - 1), which is the g.f. of A179525.
%H A207571 Michael De Vlieger, <a href="/A207571/b207571.txt">Table of n, a(n) for n = 0..200</a>
%H A207571 Hsien-Kuei Hwang, Emma Yu Jin, <a href="https://arxiv.org/abs/1911.06690">Asymptotics and statistics on Fishburn matrices and their generalizations</a>, arXiv:1911.06690 [math.CO], 2019.
%F A207571 a(n) ~ GAMMA(1/3) * 2^(2*n+1/3) * 3^(2*n+7/6) * n^(n+1/6) / (exp(n+Pi^2/72) * Pi^(2*n+11/6)). - _Vaclav Kotesovec_, May 06 2014
%e A207571 G.f.: A(x) = 1 + 2*x + 11*x^2 + 105*x^3 + 1390*x^4 + 23520*x^5 + 484247*x^6 +...
%e A207571 such that, by definition,
%e A207571 A(x) = 1 + ((1+x)^2-1) + ((1+x)^2-1)*((1+x)^5-1) + ((1+x)^2-1)*((1+x)^5-1)*((1+x)^8-1) + ((1+x)^2-1)*((1+x)^5-1)*((1+x)^8-1)*((1+x)^11-1) +...
%t A207571 CoefficientList[Series[Sum[Product[(1+x)^(3*k-1)-1, {k, 1, n}], {n, 0, 20}], {x, 0, 20}], x] (* _Vaclav Kotesovec_, May 06 2014 *)
%o A207571 (PARI) {a(n)=polcoeff(sum(m=0,n,prod(k=1,m,(1+x)^(3*k-1)-1) +x*O(x^n)),n)}
%o A207571 for(n=0,25,print1(a(n),", "))
%Y A207571 Cf. A179525, A207556, A207569, A207570.
%K A207571 nonn
%O A207571 0,2
%A A207571 _Paul D. Hanna_, Feb 18 2012