A323277 G.f. = (x/6)*( 1/(1-12*x)^(3/2) - 1/(1-12*x) ).

0, 0, 1, 21, 342, 5049, 70794, 961794, 12792492, 167583249, 2170496898, 27864238950, 355198394484, 4501897295274, 56786420175588, 713416451137956, 8931958558413912, 111495926008783809, 1388178160043508018, 17244120146466623166, 213776181450214477092, 2645421031806169214574

Offset: 0

Author

N. J. A. Sloane, Jan 11 2019

Keywords

• nonn

Links

• Evgeniy Krasko, Alexander Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics (2019) Vol. 342, Issue 2, 584-599. Also arXiv:1709.03225 [math.CO]. See last line of Section 2.

Programs

Mathematica

a[n_] := (2^(2n-3) 3^(n-2) ((2n-1)!!/2^(n-1) - (n-1)!))/(n-1)!; a[0] = 0;
Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2019 *)
CoefficientList[Series[x/6 (1/(1-12x)^(3/2)-1/(1-12x)),{x,0,30}],x] (* Harvey P. Dale, Jun 18 2021 *)

Formula

(-n+1)*a(n) +6*(4*n-5)*a(n-1) +72*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Jan 17 2019

a(n) = A115903(n-1)/6 - 2*A001021(n-2), n>1. - R. J. Mathar, Jan 17 2019

a(n) = (2^(2*n-3)*3^(n-2)*((2*n-1)!!/2^(n-1) - (n-1)!))/(n-1)!, n>0. - Jean-François Alcover, Feb 14 2019