A336310 - OEIS

A336310

Sum of path lengths over all labeled rooted unordered binary trees.

0, 0, 2, 24, 300, 4260, 69120, 1271340, 26233200, 601246800, 15171105600, 418203324000, 12509695598400, 403696590897600, 13982667790291200, 517482647165484000, 20381726051118432000, 851302665544050720000, 37587618060140244096000, 1749369290830388555328000, 85599487854917373617280000

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

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