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 A000222 Coefficients of ménage hit polynomials. (Formerly M2602 N1029) 2
 0, 0, 1, 3, 6, 38, 213, 1479, 11692, 104364, 1036809, 11344859, 135548466, 1755739218, 24504637741, 366596136399, 5852040379224, 99283915922264, 1783921946910417, 33840669046326579, 675849838112277598, 14174636583759324798 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198. 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 Alois P. Heinz, Table of n, a(n) for n = 0..150 R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976 FORMULA a(n) ~ 2/exp(2) * n!. - Vaclav Kotesovec, Sep 06 2014 a(n)+2*a(n+p)+a(n+2*p) is divisible by p for any prime p. - Mark van Hoeij, Jun 13 2019 MATHEMATICA max = 30; f[x_, y_] := Sum[n!*((x*y)^n/(1+x*(y-1))^(2*n+1)), {n, 0, max}]; t = MapIndexed[Take[#1, First[#2]]&, CoefficientList[Series[f[x, y], {x, 0, max}, {y, 0, max}], {x, y}]] ; a[0] = a[1] = 0; a[n_] := t[[n+1, n-1]]; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Mar 11 2014, after Vladeta Jovovic *) CROSSREFS A diagonal of A058057. Sequence in context: A025596 A172361 A114038 * A208649 A203178 A104271 Adjacent sequences: A000219 A000220 A000221 * A000223 A000224 A000225 KEYWORD nonn AUTHOR N. J. A. Sloane, Simon Plouffe STATUS approved

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Last modified June 7 10:34 EDT 2023. Contains 363157 sequences. (Running on oeis4.)