|
%I M2076 N0820 #27 Jun 10 2019 22:59:36
%S 2,15,60,469,3660,32958,328920,3614490,43341822,563144725,7880897892,
%T 118177520295,1890389939000,32130521850972,578260307815920,
%U 10985555094348948,219687969344126490,4613039009310624795,101479234383619208204,2333872309936442446905
%N Coefficients of ménage hit polynomials.
%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Sean A. Irvine, <a href="/A000181/b000181.txt">Table of n, a(n) for n = 4..250</a>
%F Conjecture: 3*(2111*n-8303)*(n-4)*(-9+2*n)^2*a(n) - (n-3)*(25332*n^4 - 377236*n^3 + 1898681*n^2 - 3320738*n + 484000)*a(n-1) - 2*(n-4)*(12140*n^4 - 118152*n^3 + 337063*n^2 - 377436*n + 225720)*a(n-2) + (1052*n^5 - 40656*n^4 + 266063*n^3 - 549153*n^2 + 49850*n + 655200)*a(n-3) +(263*n+640)*(n-3)*(-7+2*n)^2*a(n-4) = 0. - _R. J. Mathar_, Nov 02 2015
%F Conjecture: a(n) + 2*a(n+p) + a(n+2*p) is divisible by p for any prime p > 3. - _Mark van Hoeij_, Jun 10 2019
%Y A diagonal of A058087. Cf. A000179, A000425.
%K nonn
%O 4,1
%A _N. J. A. Sloane_, _Simon Plouffe_
|
