A323277 - OEIS

%I #16 Jun 18 2021 15:13:20

%S 0,0,1,21,342,5049,70794,961794,12792492,167583249,2170496898,

%T 27864238950,355198394484,4501897295274,56786420175588,

%U 713416451137956,8931958558413912,111495926008783809,1388178160043508018,17244120146466623166,213776181450214477092,2645421031806169214574

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

%H Evgeniy Krasko, Alexander Omelchenko, <a href="https://doi.org/10.1016/j.disc.2018.07.013">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</a>, Discrete Mathematics (2019) Vol. 342, Issue 2, 584-599. Also <a href="https://arxiv.org/abs/1709.03225">arXiv:1709.03225 [math.CO]</a>. See last line of Section 2.

%F (-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

%F a(n) = A115903(n-1)/6 - 2*A001021(n-2), n>1. - _R. J. Mathar_, Jan 17 2019

%F 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

%t a[n_] := (2^(2n-3) 3^(n-2) ((2n-1)!!/2^(n-1) - (n-1)!))/(n-1)!; a[0] = 0;

%t Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Feb 14 2019 *)

%t CoefficientList[Series[x/6 (1/(1-12x)^(3/2)-1/(1-12x)),{x,0,30}],x] (* _Harvey P. Dale_, Jun 18 2021 *)

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jan 11 2019