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 A202835 E.g.f.: exp(9*x/(1-2*x)) / sqrt(1-4*x^2). 7
 1, 9, 121, 2025, 40401, 927369, 24000201, 689220009, 21710549025, 743187098889, 27441452694681, 1086166287819369, 45846179189949681, 2054407698719865225, 97357866191666622441, 4862830945258077841449, 255239441235423753980481, 14040944744510973314880009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = A083886(n)^2, where the e.g.f. of A083886 is exp(3*x + x^2). a(n) = ( Sum_{k=0..[n/2]} 3^(n-2*k) * n!/((n-2*k)!*k!) )^2. a(n) ~ n^n*exp(3*sqrt(2*n)-9/4-n)*2^(n-1). - Vaclav Kotesovec, May 23 2013 D-finite with recurrence: a(n) = (2*n+7)*a(n-1) + 2*(n-1)*(2*n+7)*a(n-2) - 8*(n-1)*(n-2)^2*a(n-3). - Vaclav Kotesovec, May 23 2013 EXAMPLE E.g.f.: A(x) = 1 + 9*x + 121*x^2/2! + 2025*x^3/3! + 40401*x^4/4! +... where A(x) = 1 + 3^2*x + 11^2*x^2/2! + 45^2*x^3/3! + 201^2*x^4/4! + 963^2*x^5/5! +...+ A083886(n)^2*x^n/n! +... MATHEMATICA CoefficientList[Series[Exp[9*x/(1-2*x)]/Sqrt[1-4*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, May 23 2013 *) PROG (PARI) {a(n)=n!*polcoeff(exp(9*x/(1-2*x)+x*O(x^n))/sqrt(1-4*x^2+x*O(x^n)), n)} (PARI) {a(n)=n!^2*polcoeff(exp(3*x+x^2+x*O(x^n)), n)^2} (PARI) {a(n)=sum(k=0, n\2, 3^(n-2*k)*n!/((n-2*k)!*k!))^2} CROSSREFS Cf. A083886, A202827, A202828, A202829, A202831, A202833, A202836. Sequence in context: A046184 A084769 A246467 * A321847 A050353 A112941 Adjacent sequences:  A202832 A202833 A202834 * A202836 A202837 A202838 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 25 2011 STATUS approved

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Last modified April 11 03:12 EDT 2021. Contains 342886 sequences. (Running on oeis4.)