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A135758
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Catalan numbers at triangular positions: a(n) = A000108(n(n+1)/2).
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3
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1, 1, 5, 132, 16796, 9694845, 24466267020, 263747951750360, 11959798385860453492, 2257117854077248073253720, 1759414616608818870992479875972, 5632681584560312734993915705849145100
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = C(n(n+1), n(n+1)/2) / [n(n+1)/2 + 1].
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=binomial(n*(n+1), n*(n+1)/2)/(n*(n+1)/2+1)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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