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

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

Offset

0,2

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.

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 *)

Crossrefs

Cf. A144416.

Sequence in context: A104403 A396045 A301609 * A327053 A135444 A333041

Adjacent sequences: A144419 A144420 A144421 * A144423 A144424 A144425

Keyword

nonn

Author

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

Status

approved