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
Keywords
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.
Programs
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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
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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 *) -
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)