A124043 Number of permutations of n distinct letters (ABCD...) each of which appears thrice with three fixed points.

1, 0, 435, 90944, 40563765, 32659846104, 43036380310735, 86514409614060000, 251739515511526387401, 1017865281673593548065520, 5534999211214597734889370091, 39411238922605740572075832485280

Offset: 0

Author

Zerinvary Lajos, Nov 02 2006

Keywords

• nonn

Examples

			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;