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A207556 G.f.: Sum_{n>=0} (1+x)^n * Product_{k=1..n} ((1+x)^k - 1). 4

%I

%S 1,1,3,11,55,339,2499,21433,209717,2305719,28141925,377579731,

%T 5523750291,87508680045,1492510215135,27266981038343,531245913925837,

%U 10995334516297279,240925208376757203,5571653169126500083,135617881389268715939,3465772763274106884733

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

%C Compare g.f. to: Sum_{n>=0} Product_{k=1..n} ((1+x)^k - 1), which is the g.f. of A179525.

%H Vaclav Kotesovec, <a href="/A207556/b207556.txt">Table of n, a(n) for n = 0..170</a>

%H 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 a(n) ~ 2 * 12^(n+1) * n^(n+1/2) / (exp(n+Pi^2/24) * Pi^(2*n+3/2)). - _Vaclav Kotesovec_, May 07 2014

%e G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 55*x^4 + 339*x^5 + 2499*x^6 +...

%e such that, by definition,

%e A(x) = 1 + (1+x)*((1+x)-1) + (1+x)^2*((1+x)-1)*((1+x)^2-1) + (1+x)^3*((1+x)-1)*((1+x)^2-1)*((1+x)^3-1) + (1+x)^4*((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)*((1+x)^4-1) +...

%o (PARI) {a(n)=polcoeff(sum(m=0,n,(1+x)^m*prod(k=1,m,(1+x)^k-1) +x*O(x^n)),n)}

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A179525, A207557.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 18 2012

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Last modified December 3 16:20 EST 2020. Contains 338906 sequences. (Running on oeis4.)