A124007 Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-3 fixed points.

0, 0, 54, 216, 540, 1080, 1890, 3024, 4536, 6480, 8910, 11880, 15444, 19656, 24570

Offset: 0

Author

Zerinvary Lajos, Nov 01 2006

Keywords

• nonn

Examples

			Maple produces the following triangle - the entries in quotes give the sequence:
1
"0", 0, 0, 1
1, 0, 9, "0", 9, 0, 1
56, 216, 378, 435, 324, 189, "54", 27, 0, 1
13833, 49464, 84510, 90944, 69039, 38448, 16476, 5184, 1431, "216", 54, 0, 1
6699824, 23123880, 38358540, 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, "540", 90, 0, 1
etc...
		

Crossrefs

Cf. A059058, A027468, A059073, A000459.

Programs

Maple

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;