A000181 Coefficients of ménage hit polynomials.

2, 15, 60, 469, 3660, 32958, 328920, 3614490, 43341822, 563144725, 7880897892, 118177520295, 1890389939000, 32130521850972, 578260307815920, 10985555094348948, 219687969344126490, 4613039009310624795, 101479234383619208204, 2333872309936442446905

Offset: 4

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Table of n, a(n) for n = 4..250

Crossrefs

A diagonal of A058087. Cf. A000179, A000425.

Formula

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

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