A116221 If X_1,...,X_n is a partition of a 5n-set X into 5-blocks then a(n) is equal to the number of permutations f of X such that f(X_i) <> X_i, (i=1,...,n).

0, 3614400, 1306371456000, 2432274637386240000, 15509750490368582860800000, 265241692266421512138485760000000, 10332925158674345473855915900600320000000, 815905363532798455769292988741440720076800000000, 119621339682330952236606797649198078512534126592000000000

Offset: 1

Author

Milan Janjic, Apr 09 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..89
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Crossrefs

Cf. A116218, A116219, A116220.

Programs

GAP

List([1..20], n-> Sum([0..n], j-> (-120)^j*Binomial(n,j)* Factorial(5*n-5*j))); # G. C. Greubel, May 11 2019

Magma

[(&+[(-120)^j*Binomial(n, j)*Factorial(5*n-5*j): j in [0..n]]): n in [1..20]]; // G. C. Greubel, May 11 2019

Maple

a:=n->sum((-120)^i*binomial(n,i)*(5*n-5*i)!,i=0..n).

Mathematica

Table[Sum[(-5!)^j*Binomial[n, j]*(5*n-5*j)!, {j,0,n}], {n,1,20}] (* G. C. Greubel, May 11 2019 *)

PARI

{a(n) = sum(j=0,n, (-120)^j*binomial(n,j)*(5*(n-j))!)}; \\ G. C. Greubel, May 11 2019

Sage

[sum((-120)^j*binomial(n,j)*factorial(5*n-5*j) for j in (0..n)) for n in (1..20)] # G. C. Greubel, May 11 2019

Formula

a(n) = Sum_{j=0..n} (-120)^j*binomial(n,j)*(5*n-5*k)!.