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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

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

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified August 18 12:40 EDT 2017. Contains 290720 sequences.