A069015 a(n) = n! * 3^n * Sum_{i=1..n} 1/(i * 3^i).
1, 7, 65, 786, 11814, 212772, 4468932, 107259408, 2896044336, 86881692960, 2867099496480, 103215621790080, 4025409728814720, 169067214837239040, 7608024754854048000, 365185189540668672000, 18624444687496892160000
Offset: 1
Programs
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Mathematica
Rest[CoefficientList[Series[-Log[1-x]/(1-3*x), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 05 2013 *)
Formula
E.g.f.: -log(1-x)/(1-3*x). - Vladeta Jovovic, Feb 07 2003
a(n) ~ n! * 3^n * log(3/2). - Vaclav Kotesovec, Oct 05 2013
From Seiichi Manyama, May 22 2025: (Start)
a(n) = 3 * n * a(n-1) + (n-1)!.
a(n) = (4*n-1) * a(n-1) - 3 * (n-1)^2 * a(n-2). (End)