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A070531
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Generalized Bell numbers B_{4,3}.
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3
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OFFSET
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1,2
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LINKS
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FORMULA
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In Maple notation, a(n)=(1/12)*n!*(n+1)!*(n+2)!*hypergeom([n+1, n+2, n+3], [2, 3, 4], 1)/exp(1)).
a(n)=sum(A090440(n, k), k=3..3*n)= sum((1/k!)*product(fallfac(k+(j-1)*(4-3), 3), j=1..n), k=3..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=4, s=3. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.
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MATHEMATICA
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ff[n_, k_] = Pochhammer[n - k + 1, k]; a[1, 3] = 1; a[n_, k_] := a[n, k] = Sum[Binomial[3, p]*ff[(n - 1 - p + k), 3 - p]*a[n - 1, k - p], {p, 0, 3} ]; a[n_ /; n < 2, _] = 0; Table[Sum[a[n, k] , {k, 3, 3 n}], {n, 1, 9}] (* Jean-François Alcover, Sep 01 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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