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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).
1
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Jun 19 2013
STATUS
approved