A226854 a(n) = (-5*B(n+2) + (2*n+9)*B(n+1) + (2*n+1)*B(n))/4, where the B(i) are Bell numbers (A000110).

0, 0, 0, 0, 1, 11, 89, 660, 4795, 35067, 261505, 2001608, 15777434, 128270836, 1076208942, 9318227402, 83230080505, 766465520673, 7272362469647, 71040825568988, 713933196773609

Offset

0,6

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[(-5 BellB[n+2] + (2 n + 9) BellB[n + 1] + (2 n + 1) BellB[n])/4, {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) = (-5*B(n+2) + (2*n+9)*B(n+1) + (2*n+1)*B(n))/4
(Magma) [(-5*Bell(n+2)+(2*n+9)*Bell(n+1)+(2*n+1)*Bell(n))/4: n in [0..30]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Sequence in context: A121155 A201117 A081657 * A037580 A155607 A356323

Adjacent sequences: A226851 A226852 A226853 * A226855 A226856 A226857

Keyword

nonn

Author

Michel Marcus, Jun 19 2013

Status

approved