A116219 If X_1,...,X_n is a partition of a 3n-set X into 3-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, 684, 350352, 470444112, 1293433432704, 6355554535465920, 50823027472983319296, 618002474327361540442368, 10855431334634213344062394368, 264600531449039456516679858441216, 8665832467934840277899318819803484160, 371368757645100314808527266212241861300224

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..149

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Formula

a(n) = Sum_{j=0..n} (-6)^j*binomial(n,j)*(3*n-3*j)!.

Maple

a:=n->sum((-6)^i*binomial(n, i)*(3*n-3*i)!, i=0..n).

Mathematica

Table[Sum[(-6)^i*Binomial[n, i]*(3*n - 3*i)!, {i, 0, n}], {n, 1, 20}] (* G. C. Greubel, May 11 2019 *)

Prog

(PARI) {a(n) = sum(j=0, n, (-6)^j*binomial(n, j)*(3*(n-j))!)}; \\ G. C. Greubel, May 11 2019
(Magma) [(&+[(-6)^j*Binomial(n, j)*Factorial(3*n-3*j): j in [0..n]]): n in [1..20]]; // G. C. Greubel, May 11 2019
(Sage) [sum((-6)^j*binomial(n, j)*factorial(3*n-3*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-> (-6)^j*Binomial(n, j)* Factorial(3*n-3*j))) # G. C. Greubel, May 11 2019

Crossrefs

Cf. A116218, A116220, A116221, A127888.

Sequence in context: A254071 A022050 A107514 * A232199 A222751 A234817

Adjacent sequences: A116216 A116217 A116218 * A116220 A116221 A116222

Keyword

nonn

Author

Milan Janjic, Apr 09 2007

Status

approved