Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Oct 06 2016 12:31:58
%S 1,0,435,90944,40563765,32659846104,43036380310735,86514409614060000,
%T 251739515511526387401,1017865281673593548065520,
%U 5534999211214597734889370091,39411238922605740572075832485280
%N Number of permutations of n distinct letters (ABCD...) each of which appears thrice with three 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 0,3
%A _Zerinvary Lajos_, Nov 02 2006