A125107 Subtract compositions (A011782) from Catalan numbers (A000108).

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

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