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URL: https://oeis.org/A116221

⇱ A116221 - OEIS

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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).
3
0, 3614400, 1306371456000, 2432274637386240000, 15509750490368582860800000, 265241692266421512138485760000000, 10332925158674345473855915900600320000000, 815905363532798455769292988741440720076800000000, 119621339682330952236606797649198078512534126592000000000
OFFSET
1,2
FORMULA
a(n) = Sum_{j=0..n} (-120)^j*binomial(n,j)*(5*n-5*k)!.
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 *)
PROG
(PARI) {a(n) = sum(j=0, n, (-120)^j*binomial(n, j)*(5*(n-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
(SageMath) [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
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Milan Janjic, Apr 09 2007
STATUS
approved