A225591 a(n) = B(n+3) - 6*B(n+2) + 8*B(n+1)*B(n+1) - B(n), where the B(i) are Bell numbers (A000110).

0, 16, 160, 1686, 21276, 328498, 6149136, 137105016, 3577543452, 107601726030, 3683660206080, 142035221781402, 6113719409724768, 291540411275223912, 15300594717301253800, 878667035554110785662, 54932693182800769213284

Offset

0,2

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[BellB[n+3] - 6 BellB[n+2] + 8 BellB[n+1] BellB[n+1] - BellB[n], {n, 0, 20}] (* Vincenzo Librandi, Jul 16 2013 *)
#[[4]]-6#[[3]]+8#[[2]]^2-#[[1]]&/@Partition[BellB[Range[0, 20]], 4, 1] (* Harvey P. Dale, Nov 01 2016 *)

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) = B(n+3) - 6*B(n+2) + 8*B(n+1)*B(n+1) - B(n)
(Magma) [Bell(n+3)-6*Bell(n+2)+8*Bell(n+1)*Bell(n+1)-Bell(n): n in [0..20]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Cf. A005493, A226506 (see Prop 3.1 (i) in Chern et al. link).

Sequence in context: A079767 A079768 A053410 * A197677 A197535 A204297

Adjacent sequences: A225588 A225589 A225590 * A225592 A225593 A225594

Keyword

nonn

Author

Michel Marcus, Jun 19 2013

Status

approved