A144422 a(n) = n!*A144416(n).

1, 3, 62, 5052, 1087104, 487424520, 393702654960, 519740602925040, 1046019551260199040, 3046052768591313895680, 12322848899623787148556800, 67036205966744406283600262400, 477463744343745629221074425625600, 4354451197836949908463868034925593600

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 08 2008, corrected Jan 14 2009

Keywords

• nonn

Comments

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

Links

• David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 0..100
• Samuele Giraudo and Yannic Vargas, Operads of packed words, quotients, and monomial bases, Proc. 37th Conf. Formal Power Series Alg. Comb., Sém. Lotharingien Combin. (2025) Vol. 93B Art. No. 82. See p. 9.

Crossrefs

Cf. A144416.

Programs

Mathematica

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 *)