A123280 - OEIS

%I #2 Oct 09 2013 02:24:29

%S 0,16,4536,8607744,42506546320,456702275019600,9418598754396188616,

%T 340409678708013417037696,20126978659582117984569511584,

%U 1844705433432528416880778883815440

%N Number of permutations of n distinct letters (ABCD...) each of which appears 4 times and having two fixed points.

%e 1

%e 0, 0, "0", 0, 1

%e 1, 0, "16", 0, 36, 0, 16, 0, 1

%e 346, 1824, "4536", 7136, 7947, 6336, 3936, 1728, 684, 128, 48, 0, 1

%e 748521, 3662976, "8607744", 12880512, 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, 512, 96, 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 5 do seq(coeff(f(t, n, 4), t, m)/4!^n, m=0..4*n); od;

%Y Cf. A059060.

%K nonn

%O 0,2

%A _Zerinvary Lajos_, Nov 07 2006