A135758 Catalan numbers at triangular positions: a(n) = A000108(n(n+1)/2).

1, 1, 5, 132, 16796, 9694845, 24466267020, 263747951750360, 11959798385860453492, 2257117854077248073253720, 1759414616608818870992479875972, 5632681584560312734993915705849145100

Offset: 0

Author

Paul D. Hanna, Dec 02 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000108, A135757.

Programs

Mathematica

With[{nn=100},Join[{1},Pick[CatalanNumber[Range[nn]],Array[ IntegerQ[ (Sqrt[1+8#]-1)/2]&,nn]]]] (* Harvey P. Dale, Sep 24 2011 *)
Table[Binomial[n*(n + 1), n*(n + 1)/2]/(1 + Binomial[n + 1, 2]), {n,0,10}] (* G. C. Greubel, Nov 07 2016 *)

PARI

a(n)=binomial(n*(n+1),n*(n+1)/2)/(n*(n+1)/2+1)

Formula

a(n) = C(n(n+1), n(n+1)/2) / [n(n+1)/2 + 1].