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%I #4 Oct 06 2016 12:30:33
%S 9,189,1431,5355,14310,31374,60354,105786,172935,267795,397089,568269
%N Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-4 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 0,1
%A _Zerinvary Lajos_, Nov 01 2006
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