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A000185 Coefficients of ménage hit polynomials.
(Formerly M2135 N0847)
2

%I M2135 N0847

%S 2,24,140,1232,11268,115056,1284360,15596208,204710454,2888897032,

%T 43625578836,702025263328,11993721979336,216822550325472,

%U 4135337882588880,82986434235959712,1747976804189353962,38559791049947726328,889047923669760546140

%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="/A000185/b000185.txt">Table of n, a(n) for n = 5..250</a>

%F Conjecture: +4*(210968408*n^2 -1603518486*n +2343057493) *a(n) +(-843873632*n^3 -4039256254*n^2 +144382575631*n -553812368850) *a(n-1) +(10453330198*n^3 -175111274403*n^2 +798927275864*n -639098546595) *a(n-2) +(10059264970*n^3 -98879552663*n^2 +170576803994*n -134993524720) *a(n-3) +(470894110*n^3 -5178116941*n^2 +108179055193*n -215961878286) *a(n-4) +(1708832970*n^3 -29554327949*n^2 +137453332457*n -152801514054) *a(n-5) +3*(569610990*n^2 -3742686463*n +4740040723) *a(n-6)=0. - _R. J. Mathar_, Nov 02 2015

%F 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

%F 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

%Y A diagonal of A058087. Cf. A000179, A000425.

%K nonn

%O 5,1

%A _N. J. A. Sloane_, _Simon Plouffe_

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Last modified December 5 22:37 EST 2019. Contains 329782 sequences. (Running on oeis4.)