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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..110
- Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Programs
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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
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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
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Maple
a:=n->sum((-24)^i*binomial(n,i)*(4*n-4*i)!,i=0..n).
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Mathematica
Table[Sum[(-24)^j*Binomial[n, j]*(4*n-4*j)!, {j,0,n}], {n, 1, 20}] (* G. C. Greubel, May 11 2019 *) -
PARI
{a(n) = sum(j=0,n, (-24)^j*binomial(n,j)*(4*(n-j))!)}; \\ 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
Formula
a(n) = Sum_{j=0..n} (-24)^j*binomial(n,j)*(4*n-4*j)!.