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A135758 Catalan numbers at triangular positions: a(n) = A000108(n(n+1)/2). 3
1, 1, 5, 132, 16796, 9694845, 24466267020, 263747951750360, 11959798385860453492, 2257117854077248073253720, 1759414616608818870992479875972, 5632681584560312734993915705849145100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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 *)

PROG

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

CROSSREFS

Cf. A000108, A135757.

Sequence in context: A191409 A003372 A187357 * A152794 A053517 A296191

Adjacent sequences:  A135755 A135756 A135757 * A135759 A135760 A135761

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Dec 02 2007

STATUS

approved

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Last modified October 4 12:02 EDT 2022. Contains 357239 sequences. (Running on oeis4.)