A116220 If X_1,...,X_n is a partition of a 4n-set X into 4-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, 39744, 476126208, 20876944084992, 2430394026897309696, 620098244484731975761920, 304784138698487640049544331264, 263072308376236973471661993731555328, 371936496850567880606221498503260339699712, 815826011669313721421241471652159968573722198016

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..110

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Formula

a(n) = Sum_{j=0..n} (-24)^j*binomial(n,j)*(4*n-4*j)!.

Maple

a:=n->sum((-24)^i*binomial(n, i)*(4*n-4*i)!, i=0..n).

Mathematica

Table[Sum[(-24)^j*Binomial[n, j]*(4*n-4*j)!, {j, 0, n}], {n, 1, 20}] (* G. C. Greubel, May 11 2019 *)

Prog

(PARI) {a(n) = sum(j=0, n, (-24)^j*binomial(n, j)*(4*(n-j))!)}; \\ G. C. Greubel, May 11 2019
(Magma) [(&+[(-24)^j*Binomial(n, j)*Factorial(4*n-4*j): j in [0..n]]): n in [1..20]]; // G. C. Greubel, May 11 2019
(Sage) [sum((-24)^j*binomial(n, j)*factorial(4*n-4*j) for j in (0..n)) for n in (1..20)] # G. C. Greubel, May 11 2019
(GAP) List([1..20], n-> Sum([0..n], j-> (-24)^j*Binomial(n, j)* Factorial(4*n-4*j))) # G. C. Greubel, May 11 2019

Crossrefs

Cf. A116218, A116219, A116221.

Sequence in context: A204311 A235255 A234920 * A103809 A257192 A257185

Adjacent sequences: A116217 A116218 A116219 * A116221 A116222 A116223

Keyword

nonn

Author

Milan Janjic, Apr 09 2007

Status

approved