%I #4 Oct 06 2016 12:31:08

%S 0,0,216,49464,23123880,19180338840,25791442770240,52614269909090064,

%T 154809621283047068016,631429039396055199165840,

%U 3457808596178310768284115720,24763433580060911383347280813320

%N Number of permutations of n distinct letters (ABCD...) each of which appears thrice with one fixed point.

%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