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A000222 Coefficients of ménage hit polynomials.
(Formerly M2602 N1029)

%I M2602 N1029

%S 0,0,1,3,6,38,213,1479,11692,104364,1036809,11344859,135548466,

%T 1755739218,24504637741,366596136399,5852040379224,99283915922264,

%U 1783921946910417,33840669046326579,675849838112277598,14174636583759324798

%N Coefficients of ménage hit polynomials.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A000222/b000222.txt">Table of n, a(n) for n = 0..150</a>

%H R. C. Read, <a href="/A000684/a000684_1.pdf">Letter to N. J. A. Sloane, Oct. 29, 1976</a>

%F a(n) ~ 2/exp(2) * n!. - _Vaclav Kotesovec_, Sep 06 2014

%F a(n)+2*a(n+p)+a(n+2*p) is divisible by p for any prime p. - _Mark van Hoeij_, Jun 13 2019

%t 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_ *)

%Y A diagonal of A058057.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, _Simon Plouffe_

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)