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A000185
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Coefficients of ménage hit polynomials.
(Formerly M2135 N0847)
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2
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2, 24, 140, 1232, 11268, 115056, 1284360, 15596208, 204710454, 2888897032, 43625578836, 702025263328, 11993721979336, 216822550325472, 4135337882588880, 82986434235959712, 1747976804189353962, 38559791049947726328, 889047923669760546140
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OFFSET
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5,1
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REFERENCES
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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).
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LINKS
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FORMULA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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