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 A208816 G.f.: Sum_{n>=0} Prod_{k=1..n} ((1+2*x)^k - 1)/((1+2*x)^k + 1). 1
 1, 1, 1, 3, 9, 39, 193, 1135, 7585, 57055, 476161, 4366399, 43627393, 471693439, 5486186497, 68296367871, 906012795393, 12758750871039, 190081374027777, 2986828127798271, 49367131036252161, 856162355062638591, 15545263081776742401, 294905583408022810623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..200 FORMULA 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 EXAMPLE G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 9*x^4 + 39*x^5 + 193*x^6 + 1135*x^7 +... PROG (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)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Sequence in context: A287063 A080635 A278749 * A130905 A030799 A273396 Adjacent sequences:  A208813 A208814 A208815 * A208817 A208818 A208819 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 01 2012 STATUS approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)