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 A137962 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^3. 6
 1, 1, 3, 18, 106, 720, 5085, 37493, 284331, 2204973, 17404720, 139369905, 1129411314, 9244823986, 76326154857, 634847759955, 5314684735045, 44746683774474, 378652035541761, 3218705637379698, 27471657413667780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..350 FORMULA G.f.: A(x) = 1 + x*B(x)^3 where B(x) is the g.f. of A137963. a(n) = Sum_{k=0..n-1} C(3*(n-k),k)/(n-k) * C(5*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009 a(n) ~ sqrt(3*s*(1-s)*(5-6*s) / ((140*s - 120)*Pi)) / (n^(3/2) * r^n), where r = 0.1085884782751570249717333800652227343328635496829... and s = 1.301018963559115613510052458264916439485131890857... are real roots of the system of equations s = 1 + r*(1 + r*s^5)^3, 15 * r^2 * s^4 * (1 + r*s^5)^2 = 1. - Vaclav Kotesovec, Nov 22 2017 PROG (PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*(1+x*A^5)^3); polcoeff(A, n)} (PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(3*(n-k), k)/(n-k)*binomial(5*k, n-k-1))) \\ Paul D. Hanna, Jun 16 2009 CROSSREFS Cf. A137963, A137961; A137953, A137957, A137969. Sequence in context: A007277 A025595 A151331 * A267662 A169604 A081341 Adjacent sequences:  A137959 A137960 A137961 * A137963 A137964 A137965 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 26 2008 STATUS approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)