A046996 Number of Baxter permutations: A001181/2.

1, 3, 11, 46, 211, 1037, 5377, 29101, 163120, 941480, 5570280, 33664996, 207249719, 1296670793, 8229378293, 52895993341, 343891293422, 2258771535962, 14974619271658, 100117092310368, 674548712552456, 4577138309318008, 31261253291922136, 214800030086785976

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1120

Crossrefs

Cf. A359363.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, 2*n-3,
      ((7*n^2+7*n-2)*a(n-1)+8*(n-1)*(n-2)*a(n-2))/((n+2)*(n+3)))
    end:
seq(a(n), n=2..25);  # Alois P. Heinz, Jul 29 2022

Mathematica

Sum[Binomial[n+1, k-1] Binomial[n+1, k] Binomial[n+1, k+1], {k, 1, n}]/(2 Binomial[n+1, 1] Binomial[n+1, 2])

SageMath

def A046996(n): return PolyA359363(n, 1) // 2
print([A046996(n) for n in range(2, 26)])  # Peter Luschny, Jan 04 2024

Formula

a(n) = (1/2)*B(n, 1) where B(n, x) are the Baxter polynomials with coefficients A359363. - Peter Luschny, Jan 04 2024

Extensions

More terms from Olivier Gérard, Jun 26 2001