A226855 a(n) = n*B(n-1) + n*(n-1)*B(n-2), where the B(i) are Bell numbers (A000110).

0, 1, 4, 12, 44, 175, 762, 3605, 18384, 100404, 584070, 3601895, 23451540, 160633681, 1153896772, 8668821600, 67943174000, 554327140739, 4698491153454, 41299244789989, 375844030441560

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

B. Chern, P. Diaconis, D. M. Kane, R. C. Rhoades, Closed expressions for averages of set partition statistics, 2013.

Mathematica

Table[n BellB[n-1] + n (n-1) BellB[n-2], {n, 0, 30}] (* Vincenzo Librandi, Jul 16 2013 *)

Prog

(PARI) B(n) = if (n<=1, return (1), return (sum(i=0, n-1, binomial(n-1, i)*B(n-1-i))))
a(n) = n*B(n-1) + n*(n-1)*B(n-2)
(Magma) [0, 1] cat [n*Bell(n-1)+n*(n-1)*Bell(n-2): n in [2..25]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Cf. A052889 (see Prop 3.1 (ii) in Chern et al. link).

Sequence in context: A000759 A076793 A007860 * A039740 A065143 A098543

Adjacent sequences: A226852 A226853 A226854 * A226856 A226857 A226858

Keyword

nonn

Author

Michel Marcus, Jun 19 2013

Status

approved