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 A000185 Coefficients of ménage hit polynomials. (Formerly M2135 N0847) 2
 2, 24, 140, 1232, 11268, 115056, 1284360, 15596208, 204710454, 2888897032, 43625578836, 702025263328, 11993721979336, 216822550325472, 4135337882588880, 82986434235959712, 1747976804189353962, 38559791049947726328, 889047923669760546140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 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 = 5..250 FORMULA 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 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 CROSSREFS A diagonal of A058087. Cf. A000179, A000425. Sequence in context: A261475 A078994 A290775 * A264566 A163752 A035600 Adjacent sequences:  A000182 A000183 A000184 * A000186 A000187 A000188 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 13 00:17 EDT 2021. Contains 342934 sequences. (Running on oeis4.)