A000181 Coefficients of ménage hit polynomials. (Formerly M2076 N0820)

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

Offset

4,1

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

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

Crossrefs

A diagonal of A058087. Cf. A000179, A000425.

Sequence in context: A084169 A337905 A296661 * A047146 A084187 A267596

Adjacent sequences: A000178 A000179 A000180 * A000182 A000183 A000184

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved