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

Author

Michel Marcus, Jun 19 2013

Keywords

• nonn

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.

Crossrefs

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

Programs

Magma

[0,1] cat [n*Bell(n-1)+n*(n-1)*Bell(n-2): n in [2..25]]; // Vincenzo Librandi, Jul 16 2013

Mathematica

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

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)