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A124073 Number of permutations of n distinct letters (ABCD...) each of which appears 4 times with one fixed point. 0

%I

%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

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Last modified October 16 09:02 EDT 2021. Contains 348041 sequences. (Running on oeis4.)