A324360 Total number of occurrences of 10 in the (signed) displacement sets of all permutations of [n+10] divided by 10!.

0, 1, 21, 364, 6115, 104226, 1834205, 33576236, 641293047, 12792063934, 266464077769, 5792423481120, 131276423686979, 3098383343174978, 76066855087291221, 1940223116685166996, 51356370210296015215, 1409053932006095867526, 40028877611196977481857

Offset: 0

Author

Alois P. Heinz, Feb 23 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..442
• Wikipedia, Permutation

Crossrefs

Column k=10 of A324362.

Cf. A306234.

Programs

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(10):
seq(a(n), n=0..23);

Mathematica

With[{nn=20},CoefficientList[Series[(1-Exp[-x])/(1-x)^11,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 04 2023 *)

Formula

E.g.f.: (1-exp(-x))/(1-x)^11.

a(n) = -1/10! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+10-j)!.

a(n) = A306234(n+10,10).