A000425 Coefficients of ménage hit polynomials. (Formerly M4507 N1908)

2, 0, 0, 8, 30, 192, 1344, 10800, 97434, 976000, 10749024, 129103992, 1679495350, 23525384064, 353028802560, 5650370001120, 96082828074162, 1729886440780800, 32874134679574208, 657589108734075240, 13811277748363437006, 303884178002526338624

Offset

1,1

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

Table of n, a(n) for n=1..22.

Formula

It appears that a(n) = round(4*n*exp(-2)*(BesselK(n-1,2)+BesselK(n,2))) when n >= 10. - Mark van Hoeij, Oct 25 2011

Conjecture: (n-1)*(n-3)*a(n) -n*(n-2)*(n-3)*a(n-1) -n*(n-1)*(n-3)*a(n-2) -n *(n-1)*a(n-3)=0. - R. J. Mathar, Nov 02 2015

Conjecture: a(n) = 2*n*A000271(n). - R. J. Mathar, Nov 02 2015

Mathematica

p[n_] := Sum[2*n/(2*n-k)*Binomial[2*n-k, k]*(n-k)!*(x-1)^k, {k, 0, n}] // CoefficientList[#, x]&; Array[p, 25][[All, 2]] (* Jean-François Alcover, Feb 08 2016 *)

Crossrefs

A diagonal of A058087. Cf. A000179.

Sequence in context: A236925 A134414 A113036 * A230878 A349369 A349352

Adjacent sequences: A000422 A000423 A000424 * A000426 A000427 A000428

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved