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A125107 Subtract compositions (A011782) from Catalan numbers (A000108). 2
0, 0, 0, 1, 6, 26, 100, 365, 1302, 4606, 16284, 57762, 205964, 738804, 2666248, 9678461, 35324902, 129579254, 477507628, 1767001046, 6563596132, 24465218444, 91480466488, 343055419346, 1289895758716, 4861929624236, 18367319517720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Apparently the number of Dyck n-paths with more than half of the path lying between the first and last peaks. - David Scambler, Sep 14 2012

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = A000108(n) - A011782(n).

Conjecture: (n+1)*a(n) +2*(1-4*n)*a(n-1) +4*(5*n-7)*a(n-2) +8*(5-2*n)*a(n-3)=0. - R. J. Mathar, Aug 10 2013

EXAMPLE

A000108 begins 1 1 2 5 14 42 132 429 ...

A011782 begins 1 1 2 4 8 16 32 64 ...

so we get .... 0 0 0 1 6 26 100 365 ...

MATHEMATICA

Table[CatalanNumber[n] - If[n==0, 1, 2^(n-1)], {n, 0, 30}] (* David Scambler, Sep 14 2012 *)

CROSSREFS

Cf. A000079, A000108, A000110, A011782, A016098.

Sequence in context: A261064 A094811 A005022 * A301476 A290347 A034560

Adjacent sequences: A125104 A125105 A125106 * A125108 A125109 A125110

KEYWORD

easy,nonn

AUTHOR

Alford Arnold, Dec 15 2006

EXTENSIONS

More terms from David Scambler, Sep 14 2012

STATUS

approved

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Last modified February 5 22:19 EST 2023. Contains 360087 sequences. (Running on oeis4.)