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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). 2
0, 16, 160, 1686, 21276, 328498, 6149136, 137105016, 3577543452, 107601726030, 3683660206080, 142035221781402, 6113719409724768, 291540411275223912, 15300594717301253800, 878667035554110785662, 54932693182800769213284 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 06:44 EST 2022. Contains 358362 sequences. (Running on oeis4.)