A174663 a(n) is the number of solutions to the congruence Sum_{k=1..n} x_k == 1 (mod 2n), where x_k are distinct elements of the set {0, 1, ..., 2n}, k = 1..n.

1, 4, 18, 192, 3000, 56160, 1234800, 32256000, 979776000, 33566400000, 1279932192000, 53950908211200, 2490951541478400, 124914111972249600, 6761428395321600000, 393000294670663680000, 24412776290272161792000, 1613964246117021646848000, 113146793781167491817472000

Offset

1,2

References

V. S. Shevelev, On number of solutions of congruence Sum{i=1,...,s}x_i==r(modk), Izvestia Vuzov of the North-Caucasus region, Nature sciences, 2 (1997), 25-37 (in Russian).

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = ((n-1)!/2)*Sum_{d|n} ( -1)^(n+d)*mu(n/d)*C(2d,d), where mu(n) is the Mobius function A008683.

Example

If n=2, then we have the congruence x_1 + x_2 == 1 (mod 4), x_i is in {0,1,2,3}. Here we have 4 solutions: (0,1), (1,0), (2,3), (3,2); therefore a(2)=4.

Prog

(PARI) a(n) = ((n-1)!/2) * sumdiv(n, d, ( -1)^(n+d) * moebius(n/d) * binomial(2*d, d) );
vector(33, n, a(n)) \\ Joerg Arndt, Sep 05 2018

Crossrefs

Cf. A008683, A000984.

Sequence in context: A260970 A154731 A201346 * A356561 A197786 A242083

Adjacent sequences: A174660 A174661 A174662 * A174664 A174665 A174666

Keyword

nonn

Author

Vladimir Shevelev, Mar 26 2010, Apr 09 2010, Jun 29 2010

Extensions

a(6) corrected and more terms from Joerg Arndt, Sep 05 2018

Status

approved