A359126 A000168(n+1) - A000139(n).

0, 8, 52, 372, 2894, 23966, 208086, 1874508, 17390158, 165248499, 1601857338, 15790898316, 157915304928, 1598927475749, 16365689821454, 169113248927772, 1762344520554606, 18504654979649615, 195620858324078190, 2080695883684277190, 22254407183551916850

Offset: 0

Author

N. J. A. Sloane, Dec 23 2022, following a suggestion from Doron Zeilberger

Keywords

• nonn

Comments

Number of separable rooted planar maps with n+1 edges. - Noam Zeilberger, Dec 26 2022

Links

• W. T. Tutte, A Census of Planar Maps, Canad. J. Math. 15 (1963), 249-271.

Crossrefs

Cf. A000139, A000168.

Programs

Maple

a := n -> 2*(3^(n + 1)*(2*n + 2)!/(n + 3)! - (3*n)!/(2*n + 1)!)/(n + 1)!:
seq(a(n), n = 0..20); # Peter Luschny, Dec 26 2022

Formula

a(n) ~ ((48^(n + 1) - 3^(3*n + 1/2)))/(2^(2*n + 1)*sqrt(Pi)*n^(5/2)). - Peter Luschny, Dec 26 2022

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