A384282 a(n) is the n-th q-Catalan number for q=n.

1, 1, 5, 847, 18245201, 100333200992026, 228658497157753687896157, 319559330566264937870155968502833579, 380933302489206359659857650468008737411766944866881, 514667012348784999156727812545930551654233884899853599864429378680766

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Formula

a(n) ~ n^(n*(n-1)). - Vaclav Kotesovec, May 29 2025

Mathematica

Table[QBinomial[2*n, n, n]/QBinomial[n+1, 1, n], {n, 0, 10}] (* Vaclav Kotesovec, May 29 2025 *)

Prog

(SageMath)
from sage.combinat.q_analogues import q_catalan_number
def a(n): return q_catalan_number(n, n)

Crossrefs

Main diagonal of A384437.

Sequence in context: A060713 A198402 A380031 * A214450 A332185 A085706

Adjacent sequences: A384279 A384280 A384281 * A384283 A384284 A384285

Keyword

nonn

Author

Seiichi Manyama, May 29 2025

Status

approved