A366924 Number of 2n-step walks on square lattice starting and ending at the origin with first step north and avoiding early returns.

1, 5, 44, 469, 5516, 68892, 896016, 11998869, 164259308, 2287663804, 32303714576, 461352451292, 6651528522256, 96669999247184, 1414652852290752, 20825721430968213, 308191001159544876, 4581880220433822108, 68398967956430765712, 1024826569020715088508, 15405900278361291658896

Offset: 1

Author

Hugo Pfoertner, Dec 05 2023

Keywords

• nonn
• walk

Crossrefs

Cf. A054474.

Programs

Maple

b:= proc(n) b(n):= binomial(2*n, n)^2 end:
a:= proc(n) option remember;
      b(n)/4-add(a(n-i)*b(i), i=1..n-1)
    end:
seq(a(n), n=1..21);  # Alois P. Heinz, Dec 05 2023

Mathematica

b[n_] := b[n] = Binomial[2*n, n]^2;
a[n_] := a[n] = b[n]/4 - Sum[a[n-i]*b[i], {i, 1, n-1}];
Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Jan 28 2025, after Alois P. Heinz *)

Formula

a(n) = A054474(n)/4.