A000222 Coefficients of ménage hit polynomials.

0, 0, 1, 3, 6, 38, 213, 1479, 11692, 104364, 1036809, 11344859, 135548466, 1755739218, 24504637741, 366596136399, 5852040379224, 99283915922264, 1783921946910417, 33840669046326579, 675849838112277598, 14174636583759324798

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn

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

Crossrefs

A diagonal of A058057.

Programs

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 *)

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