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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..149
- Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Programs
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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
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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
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Maple
a:=n->sum((-6)^i*binomial(n,i)*(3*n-3*i)!,i=0..n).
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Mathematica
Table[Sum[(-6)^i*Binomial[n, i]*(3*n - 3*i)!, {i, 0, n}], {n, 1, 20}] (* G. C. Greubel, May 11 2019 *) -
PARI
{a(n) = sum(j=0,n, (-6)^j*binomial(n,j)*(3*(n-j))!)}; \\ 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
Formula
a(n) = Sum_{j=0..n} (-6)^j*binomial(n,j)*(3*n-3*j)!.