_Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), _, Nov 07 2006

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

0, 0, 7136, 12880512, 61907282240, 654044867816320, 13334947538204224800, 477979874685352308242176, 28084174272553340151416556672, 2561385146102672068174078977972480

0,3

1

0, 0, 0, "0", 1

1, 0, 16, "0", 36, 0, 16, 0, 1

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

748521, 3662976, 8607744, "12880512", 13731616, 11042688, 6928704, 3458432, 1395126, 453888, 122016, 25344, 4824, 512, 96, 0, 1

3993445276, 18743463360, 42506546320, "61907282240", 64917874125, 52087325696, 33176621920, 17181584640, 7352761180, 2628808000, 790912656, 201062080, 43284010, 7873920, 1216000, 154496, 17640, 1280, 160, 0, 1

etc..

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;

Cf. A059060.

nonn

Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2006

approved