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 A207652 G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^k - 1)/(1 - x^k). 4
 1, 1, 3, 10, 45, 249, 1709, 13912, 131168, 1402706, 16757321, 221018769, 3188425939, 49925523804, 843121969923, 15272776193787, 295372123082865, 6073931908657770, 132329525329523223, 3044691799670213778, 73771773281455834427, 1877511491197391256001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..210 Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019. FORMULA From Vaclav Kotesovec, Oct 31 2014: (Start) a(n) ~ 6*sqrt(2) * 12^n * n! / (exp(Pi^2/24) * Pi^(2*n+2)). a(n) ~ 12^(n+1) * n^(n+1/2) / (exp(n + Pi^2/24) * Pi^(2*n+3/2)). (End) EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 45*x^4 + 249*x^5 + 1709*x^6 +... such that, by definition, A(x) = 1 + ((1+x)-1)/(1-x) + ((1+x)-1)*((1+x)^2-1)/((1-x)*(1-x^2)) + ((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)/((1-x)*(1-x^2)*(1-x^3)) +... PROG (PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, ((1+x)^k-1)/(1-x^k +x*O(x^n)) )), n)} for(n=0, 40, print1(a(n), ", ")) CROSSREFS Cf. A207651, A207653, A207654. Sequence in context: A060311 A184947 A330250 * A099237 A006220 A020026 Adjacent sequences:  A207649 A207650 A207651 * A207653 A207654 A207655 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 19 2012 STATUS approved

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Last modified June 18 15:19 EDT 2021. Contains 345120 sequences. (Running on oeis4.)