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%I #4 Oct 06 2016 12:31:33
%S 0,9,378,84510,38358540,31234760055,41467520432646,83805898840005132,
%T 244832935610272588920,993012060508835944545045,
%U 5413243051841698780829328690,38622438042365626607874252846474
%N Number of permutations of n distinct letters (ABCD...) each of which appears thrice with two fixed points.
%e 1
%e 0, 0, "0", 1
%e 1, 0, "9", 0, 9, 0, 1
%e 56, 216, "378", 435, 324, 189, 54", 27, 0, 1
%e 13833, 49464, "84510", 90944, 69039, 38448, 16476, 5184, 1431, 216, 54, 0, 1
%e 6699824, 23123880, "38358540", 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 0, 1
%e etc...
%p p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
%Y Cf. A059058, A027468, A059073, A000459.
%K nonn
%O 0,2
%A _Zerinvary Lajos_, Nov 02 2006
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