A091755 Sixth column (m=7) of array A091752 ((-1,2)Stirling2) divided by -12.
1, 140, 27720, 7847840, 3049446400, 1564366003200, 1026108219136000, 838477001922560000, 835580445006827520000, 997744946185930342400000, 1406513375677181496524800000, 2311431202054422682730496000000, 4380418953582248141850148864000000, 9483101601549384660012281888768000000
Offset: 4
Programs
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Mathematica
a[n_] := (3/(4*5!))*n*(n-3)*(3*(n-2))!/((3^(n-2))*(n-2)!); Array[a, 15, 4] (* Amiram Eldar, Aug 30 2025 *)
Formula
a(n) = -A091752(n, 7)/12, n>=4.
a(n) = (3/(4*5!))*n*(n-3)*(3*(n-2))!/((3^(n-2))*(n-2)!) = 3*n*(n-3) * A052502(n-2)/(4*5!), n>=4.
G.f.: (x^4)*hypergeom([7/3, 8/3, 5, 2], [4], 9*x).
a(n) ~ 3^(2*n-7/2) * n^(2*n-2) /(160 * exp(2*n-5/n)). - Amiram Eldar, Aug 30 2025