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E. E. Kummer, <a href="https://doi.org/10.1515/crll.1852.44.93">Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen</a>, Journal für die reine und angewandte Mathematik, Vol. 44 (1852), pp. 93-146; <a href="https://eudml.org/doc/147500">alternative link</a>.

Dorel Miheţ, <a href="https://doi.org/10.1007/s12045-010-0123-4">Legendre's and Kummer's theorems again</a>, Resonance, Vol. 15, No. 12 (2010), pp. 1111-1121; <a href="https://www.ias.ac.in/public/Volumes/reso/015/12/1111-1121.pdf">alternative link</a>.

Armin Straub, Victor H. Moll and Tewodros Amdeberhan, <a href="https://eudml.org/doc/278348">The p-adic valuation of k-central binomial coefficients</a>, Acta Arithmetica, Vol. 140, No. 1 (2009), pp. 31-42.

a(n) = A053735(n) - A053735(2*n)/2. - Amiram Eldar, Feb 12 2021

Cf. A000984, A005836, A007949, A053735.

3-adic valuation of binomial(2n ,2*n, n): largest k such that 3^k divides binomial(2n ,2*n, n).

Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>.

Wikipedia, <a href="https://en.wikipedia.org/wiki/Kummer&#39;s_theorem">Kummer's theorem</a>.

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3-adic valuation of binomial(2n, ,n): largest k such that 3^k divides binomial(2n, ,n).

(PARI) a(n) = valuation(binomial(2*n, n), 3)

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3-adic valuation of Cbinomial(2n,n): largest k such that 3^k divides Cbinomial(2n,n).

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