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

1,2

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.

Links

Table of n, a(n) for n=1..17.

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

Mathematica

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

Prog

(Sage) [binomial(n*n+n-1, n)/(n*n+n-1) for n in range(1, 29)]
(Python)
from math import comb
def A351501(n): return comb(m := n**2+n-1, n)//m # Chai Wah Wu, May 07 2022

Crossrefs

Closely related to A177784. See also A091144.

Diagonal of A162382. Multiple of A182316.

Sequence in context: A020557 A323118 A184361 * A124558 A020565 A377861

Adjacent sequences: A351498 A351499 A351500 * A351502 A351503 A351504

Keyword

nonn

Author

F. Chapoton, May 03 2022

Status

approved