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A261003 a(n) = A136439(n) + Catalan(n). 1
1, 2, 5, 15, 48, 160, 549, 1924, 6851, 24700, 89945, 330239, 1220884, 4540128, 16968958, 63701573, 240059998, 907760348, 3443048256, 13094812968, 49925646786, 190772846082, 730451716847, 2802033270234, 10767028435468, 41438212118088, 159711845145544, 616393788920923, 2381898673172602 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the quantity S_{n-1} as given by a literal reading of Dershowitz and Rinderknecht (2015), Equations (1) and (2). If the lower limit in the right-hand sum in Eq. (1) is changed to "h >= 2", we obtain A136439.

LINKS

Table of n, a(n) for n=1..29.

N. Dershowitz and C. Rinderknecht, The Average Height of Catalan Trees by Counting Lattice Paths, Math. Mag., 88 (No. 3, 2015), 187-195.

MAPLE

# Maple code for Equations (1) and (2) of Dershowitz and Rinderknecht (2015).

H:=proc(n, h) local b, k; b:=binomial; add(b(2*n, n+1-k*h)-2*b(2*n, n-k*h)+b(2*n, n-1-k*h), k=1..n+1); end;

S1:=n->add(H(n, h), h=1..n+1); [seq(S1(n), n=0..30)];

CROSSREFS

Cf. A000108, A136439.

Sequence in context: A289589 A071739 A268407 * A218251 A203067 A278077

Adjacent sequences:  A261000 A261001 A261002 * A261004 A261005 A261006

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 12 2015

STATUS

approved

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Last modified June 21 12:15 EDT 2021. Contains 345364 sequences. (Running on oeis4.)