Recurrence with fourth powers of binomial coefficients

formal-conjectures · oeis · ams-11

The sequence is defined by $a(1) = 2$, and for $n \ge 2$,
$$(2n+1)^3 a(n) = 32n^3 a(n-1) + (21n^3 + 22n^2 + 8n + 1) \binom{2n-1}{n}^4.$$

Each term $a(n)$ is a positive integer.
- _Zhi-Wei Sun_, Apr 06 2010

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A176477
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/0911.5665
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/176477.lean
Local target: Corpus.OEIS176477.conjecture1
Source SHA-256: a066d82ecf94499b8b59039084ae37d04c7b13d8a39147a3207a2ca1f51db547
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record