|
%I #15 Nov 09 2020 00:08:14
%S 0,0,1824,3662976,18743463360,206032439164800,4316868116405748960,
%T 157846181105000772889344,9416135162778291726755147136,
%U 869099332136838873667455070091520,118924204222864960529120670496333629600,23292190275693669075772234927951426886017920
%N Number of permutations of n distinct letters (ABCD...) each of which appears 4 times with one fixed point.
%F a(n) = A059060(n, 1). - _Joerg Arndt_, Nov 08 2020
%e A059060 as a triangle:
%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 3993445276, "18743463360", 42506546320, 61907282240, 64917874125, 52087325696, 33176621920, 17181584640, 7352761180, 2628808000, 790912656, 201062080, 43284010, 7873920, 1216000, 154496, 17640, 1280, 160, 0, 1
%p p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k);
%p R := (x, n, k)->p(x, k)^n;
%p f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k);
%p # copied from A059060
%p seq(coeff(f(t, n, 4), t, 1)/4!^n, n=1..12);
%Y Cf. A059060.
%K nonn,uned
%O 1,3
%A _Zerinvary Lajos_, Nov 05 2006
%E Offset corrected by _Joerg Arndt_, Nov 08 2020
|
