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%I #4 Oct 06 2016 12:29:49
%S 0,0,54,216,540,1080,1890,3024,4536,6480,8910,11880,15444,19656,24570
%N Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-3 fixed points.
%e Maple produces the following triangle - the entries in quotes give the sequence:
%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 0,3
%A _Zerinvary Lajos_, Nov 01 2006
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