This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A144422 #16 Aug 04 2025 10:02:05
%S A144422 1,3,62,5052,1087104,487424520,393702654960,519740602925040,
%T A144422 1046019551260199040,3046052768591313895680,
%U A144422 12322848899623787148556800,67036205966744406283600262400,477463744343745629221074425625600,4354451197836949908463868034925593600
%N A144422 a(n) = n!*A144416(n).
%C A144422 Number of placing of at least n objects but no more than 3*n distinct objects in n distinct boxes with the condition that in each box there is at least 1 object but no more than 3. - _Adi Dani_, May 04 2011
%H A144422 David Applegate and N. J. A. Sloane, <a href="/A144422/b144422.txt">Table of n, a(n) for n = 0..100</a>
%H A144422 Samuele Giraudo and Yannic Vargas, <a href="https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2025/82.pdf">Operads of packed words, quotients, and monomial bases</a>, Proc. 37th Conf. Formal Power Series Alg. Comb., Sém. Lotharingien Combin. (2025) Vol. 93B Art. No. 82. See p. 9.
%t A144422 t[n_, n_] = 1; t[n_ /; n >= 0, k_] /; 0 <= k <= 3*n := t[n, k] = t[n - 1, k - 1] + (k - 1)*t[n - 1, k - 2] + (1/2)*(k - 1)*(k - 2)*t[n - 1, k - 3]; t[_, _] = 0; a[n_] := Sum[t[n, k], {k, 0, 3*n}]; Table[n!*a[n], {n, 0, 20}] (* _Michael De Vlieger_, Aug 04 2025, after _Jean-François Alcover_ at A144416 *)
%Y A144422 Cf. A144416.
%K A144422 nonn
%O A144422 0,2
%A A144422 _David Applegate_ and _N. J. A. Sloane_, Dec 08 2008, corrected Jan 14 2009