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A143360 Sum of root degrees of all symmetric ordered trees with n edges. 1
1, 3, 5, 12, 20, 45, 77, 168, 294, 630, 1122, 2376, 4290, 9009, 16445, 34320, 63206, 131274, 243542, 503880, 940576, 1939938, 3640210, 7488432, 14115100, 28973100, 54826020, 112326480, 213286590, 436268025, 830905245, 1697168160, 3241119750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..33.

FORMULA

G.f.: z*C(z^2)^2*(1+2*z*C(z^2))/(1-z*C(z^2)), where C(z)=(1-sqrt(1-4*z))/(2*z) is the g.f. of the Catalan numbers (A000108).

a(n) = sum(k=1..n, k * A143359(n,k) ).

D-finite with recurrence 2*(n+3)*a(n) +(-n-5)*a(n-1) +(-11*n-3)*a(n-2) +2*(2*n+1)*a(n-3) +12*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 24 2022

MAPLE

C := z -> (1/2-(1/2)*sqrt(1-4*z))/z: G := z*C(z^2)^2*(1+2*z*C(z^2))/(1-z*C(z^2)): Gser := series(G, z=0, 40): seq(coeff(Gser, z, n), n=1..34);

CROSSREFS

Cf. A000108, A129869 and A143359.

Sequence in context: A089292 A309702 A358369 * A234005 A263346 A034763

Adjacent sequences: A143357 A143358 A143359 * A143361 A143362 A143363

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 15 2008

STATUS

approved

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Last modified February 7 10:30 EST 2023. Contains 360115 sequences. (Running on oeis4.)