A000185 Coefficients of ménage hit polynomials.

2, 24, 140, 1232, 11268, 115056, 1284360, 15596208, 204710454, 2888897032, 43625578836, 702025263328, 11993721979336, 216822550325472, 4135337882588880, 82986434235959712, 1747976804189353962, 38559791049947726328, 889047923669760546140

Offset: 5

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 = 5..250

Crossrefs

A diagonal of A058087. Cf. A000179, A000425.

Formula

Conjecture: +4*(210968408*n^2 -1603518486*n [phone]) *a(n) +(-843873632*n^3 -4039256254*n^2 [phone]*n -553812368850) *a(n-1) +(10453330198*n^3 -175111274403*n^2 [phone]*n -639098546595) *a(n-2) +(10059264970*n^3 -98879552663*n^2 [phone]*n -134993524720) *a(n-3) +(470894110*n^3 -5178116941*n^2 [phone]*n -215961878286) *a(n-4) +(1708832970*n^3 -29554327949*n^2 [phone]*n -152801514054) *a(n-5) +3*(569610990*n^2 -3742686463*n [phone]) *a(n-6)=0. - R. J. Mathar, Nov 02 2015

Conjecture: (241*n-1066) *(2*n-11) *(-5+n)^2 *a(n) +(-482*n^5 +10099*n^4 -79756*n^3 +285961*n^2 -426904*n +149292) *a(n-1) -(2*n-9) *(n-3) *(248*n^3 -2229*n^2 +5065*n -7134) *a(n-2) +(-14*n^5 -49*n^4 -619*n^3 +13174*n^2 -51690*n +61248) *a(n-3) -(n-3) *(n-4) *(7*n-87) *(2*n-7) *a(n-4)= 0. - R. J. Mathar, Nov 02 2015

a(n)+2*a(n+p)+a(n+2*p) is divisible by p for any prime except 3 and 5. - Mark van Hoeij, Jun 13 2019