A107869 Column 1 of triangle A107867; a(n) = binomial( n*(n+1)/2 + n+1, n).

1, 3, 15, 120, 1365, 20349, 376740, 8347680, 215553195, 6358402050, 210980549208, 7778680504140, 315502265971620, 13961746143269400, 669413654240461560, 34569147570568156800, 1912924003884628655655, 112923282067713332728110

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ n^(n-1/2) * exp(n+2-13/(6*n)) / (sqrt(Pi) * 2^(n+1/2)). - Amiram Eldar, Sep 11 2025

Mathematica

a[n_] := Binomial[n*(n+1)/2 + n+1, n]; Array[a, 15, 0] (* Amiram Eldar, Sep 11 2025 *)

Prog

(PARI) a(n)=binomial(n*(n+1)/2+n+1, n)
(SageMath) [binomial(binomial(binomial(n+1, n), n-1), n-1) for n in range(1, 19)] # Zerinvary Lajos, Nov 30 2009

Crossrefs

Cf. A107867, A107868.

Sequence in context: A260511 A093571 A093570 * A156360 A377105 A160884

Adjacent sequences: A107866 A107867 A107868 * A107870 A107871 A107872

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2005

Status

approved