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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
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).
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
Sequence in context: A260970 A154731 A201346 * A356561 A197786 A242083
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