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%I #17 Mar 18 2024 04:45:51
%S 1,1,1,3,9,39,193,1135,7585,57055,476161,4366399,43627393,471693439,
%T 5486186497,68296367871,906012795393,12758750871039,190081374027777,
%U 2986828127798271,49367131036252161,856162355062638591,15545263081776742401,294905583408022810623
%N G.f.: Sum_{n>=0} Product_{k=1..n} ((1+2*x)^k - 1)/((1+2*x)^k + 1).
%H Vaclav Kotesovec, <a href="/A208816/b208816.txt">Table of n, a(n) for n = 0..340</a>
%F a(n) ~ c * 8^n * n^(n+1) / (exp(n) * Pi^(2*n)), where c = 16*sqrt(2) / (Pi^2 * exp(Pi^2/8)) = 0.6676454503392449294235... . - _Vaclav Kotesovec_, Nov 06 2014, updated Aug 22 2017
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 9*x^4 + 39*x^5 + 193*x^6 + 1135*x^7 + ...
%o (PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, ((1+2*x)^k - 1)/((1+2*x)^k + 1 +x*O(x^n)))), n)}
%o for(n=0,30,print1(a(n),", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, Mar 01 2012