A351501 a(n) = binomial(n^2 + n - 1, n) / (n^2 + n - 1).

1, 2, 15, 204, 4095, 109668, 3689595, 149846840, 7141879503, 391139588190, 24218296445200, 1673538279265020, 127715832778905150, 10670643284149377480, 968929726650218004435, 95024894699780159868144, 10011211830149283223044015

Offset: 1

Author

F. Chapoton, May 03 2022

Keywords

• nonn

Comments

Empirical: In the ring of symmetric functions over the fraction field Q(q, t), let s(n) denote the Schur function indexed by n. Then (up to sign) a(n) is the coefficient of s(1^n) in nabla^(n) s(n) with q=t=1, where nabla denotes the "nabla operator" on symmetric functions.

Crossrefs

Closely related to A177784. See also A091144.

Diagonal of A162382. Multiple of A182316.

Programs

Mathematica

Table[With[{c=n^2+n-1},Binomial[c,n]/c],{n,20}] (* Harvey P. Dale, Jan 01 2024 *)

Python

from math import comb
def A351501(n): return comb(m := n**2+n-1,n)//m # Chai Wah Wu, May 07 2022

Sage

[binomial(n*n+n-1,n)/(n*n+n-1) for n in range(1,29)]

Formula

a(n) ~ c*exp(n-1/(6*n))*n^(n-5/2), where c = sqrt(e/(2*Pi)). - Stefano Spezia, May 04 2022

a(n) = n * A182316(n - 1). - F. Chapoton, Sep 22 2023