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A321089 G.f.: Sum_{n>=0} ((1+x)^(n+1) - 1)^n.

%I A321089 #8 Oct 04 2020 08:46:47
%S A321089 1,2,10,82,928,13406,235690,4883702,116548222,3148151702,94950591878,
%T A321089 3162966582742,115334767261792,4569294561813770,195438629679894238,
%U A321089 8975996556375735458,440572146080811981406,23015418712779922737206,1274980039012724226987966,74655326188457739033712062,4607114081638141934903219532,298862442692043953057588327202
%N A321089 G.f.: Sum_{n>=0} ((1+x)^(n+1) - 1)^n.
%H A321089 Vaclav Kotesovec, <a href="/A321089/b321089.txt">Table of n, a(n) for n = 0..375</a>
%F A321089 Sum_{n>=0} (1+x)^(n*(n+1)) / (1 + (1+x)^n)^(n+1).
%F A321089 a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = 3.1610886538654288138301722... and c = 0.8785394171057422507960514834733179025314463... - _Vaclav Kotesovec_, Oct 04 2020
%e A321089 G.f.: A(x) = 1 + 2*x + 10*x^2 + 82*x^3 + 928*x^4 + 13406*x^5 + 235690*x^6 + 4883702*x^7 + 116548222*x^8 + ...
%o A321089 (PARI) {a(n) = polcoeff( sum(k=0, n, ((1+x +x*O(x^n))^(k+1) - 1)^k), n)}
%o A321089 for(n=0, 25, print1(a(n), ", "))
%o A321089 (PARI) /* From e.g.f. infinite series: */
%o A321089 \p200 \\ set precision
%o A321089 {A = Vec(round( sum(n=0, 600, 1./(1 + (1+x +O(x^26))^(-n))^(n+1)) ))}
%o A321089 for(n=0, #A-1, print1(A[n+1], ", "))
%K A321089 nonn
%O A321089 0,2
%A A321089 _Paul D. Hanna_, Nov 04 2018