A359126 - OEIS

%I #20 Jan 25 2023 09:32:46

%S 0,8,52,372,2894,23966,208086,1874508,17390158,165248499,1601857338,

%T 15790898316,157915304928,1598927475749,16365689821454,

%U 169113248927772,1762344520554606,18504654979649615,195620858324078190,2080695883684277190,22254407183551916850

%N A000168(n+1) - A000139(n).

%C Number of separable rooted planar maps with n+1 edges. - _Noam Zeilberger_, Dec 26 2022

%H W. T. Tutte, <a href="http://dx.doi.org/10.4153/CJM-1963-029-x">A Census of Planar Maps</a>, Canad. J. Math. 15 (1963), 249-271.

%F a(n) ~ ((48^(n + 1) - 3^(3*n + 1/2)))/(2^(2*n + 1)*sqrt(Pi)*n^(5/2)). - _Peter Luschny_, Dec 26 2022

%F D-finite with recurrence -2*(389*n-1012)*(2*n+1)*(n+3)*(n+1)*a(n) +3*(14101*n^4-20062*n^3-56389*n^2+45022*n-6072)*a(n-1) +18*(-20677*n^4+100317*n^3-137223*n^2+14267*n+52524)*a(n-2) +108*(547*n-956)*(3*n-7)*(2*n-3)*(3*n-8)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2023

%p a := n -> 2*(3^(n + 1)*(2*n + 2)!/(n + 3)! - (3*n)!/(2*n + 1)!)/(n + 1)!:

%p seq(a(n), n = 0..20); # _Peter Luschny_, Dec 26 2022

%Y Cf. A000139, A000168.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 23 2022, following a suggestion from _Doron Zeilberger_.