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 A336310 Sum of path lengths over all labeled rooted unordered binary trees. 0
 0, 0, 2, 24, 300, 4260, 69120, 1271340, 26233200, 601246800, 15171105600, 418203324000, 12509695598400, 403696590897600, 13982667790291200, 517482647165484000, 20381726051118432000, 851302665544050720000, 37587618060140244096000, 1749369290830388555328000, 85599487854917373617280000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA E.g.f.: ((1 -sqrt(1 -2*z -z^2))*(1 -z -sqrt(1 -2*z -z^2)))/(z*(1 -2*z -z^2)). a(n) = Sum_{k} A336309(n,k)*k, for n>=1. a(n) ~ n!/2 * (sqrt(2) + 1)^(n+1) * (1 - sqrt((10-sqrt(2))/(Pi*n))). - Vaclav Kotesovec, Jul 17 2020 MATHEMATICA nn = 20; Range[0, nn]! CoefficientList[ Series[-(((-1 + Sqrt[1 - 2 z - z^2]) (-1 + z + Sqrt[1 - 2 z - z^2]))/(z (-1 + 2 z + z^2))), {z, 0, nn}], z] PROG (PARI) my(z='z+O('z^25)); concat([0, 0], Vec(serlaplace(((1 -sqrt(1 -2*z -z^2))*(1 -z -sqrt(1 -2*z -z^2)))/(z*(1 -2*z -z^2))))) \\ Joerg Arndt, Jul 18 2020 CROSSREFS Cf. A336309, A036774 (row sums). Sequence in context: A065101 A052739 A135389 * A065513 A246190 A246610 Adjacent sequences:  A336307 A336308 A336309 * A336311 A336312 A336313 KEYWORD nonn AUTHOR Geoffrey Critzer, Jul 17 2020 STATUS approved

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Last modified May 28 22:08 EDT 2022. Contains 354122 sequences. (Running on oeis4.)