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

0, 0, 1824, 3662976, 18743463360, 206032439164800, 4316868116405748960, 157846181105000772889344, 9416135162778291726755147136, 869099332136838873667455070091520, 118924204222864960529120670496333629600, 23292190275693669075772234927951426886017920

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = A059060(n, 1). - Joerg Arndt, Nov 08 2020

Example

A059060 as a triangle:
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

Maple

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);
# copied from A059060
seq(coeff(f(t, n, 4), t, 1)/4!^n, n=1..12);

Crossrefs

Cf. A059060.

Sequence in context: A234222 A233813 A249536 * A259950 A264215 A167266

Adjacent sequences: A124070 A124071 A124072 * A124074 A124075 A124076

Keyword

nonn,uned

Author

Zerinvary Lajos, Nov 05 2006

Extensions

Offset corrected by Joerg Arndt, Nov 08 2020

Status

approved