login
A366924
Number of 2n-step walks on square lattice starting and ending at the origin with first step north and avoiding early returns.
0
1, 5, 44, 469, 5516, 68892, 896016, 11998869, 164259308, 2287663804, 32303714576, 461352451292, 6651528522256, 96669999247184, 1414652852290752, 20825721430968213, 308191001159544876, 4581880220433822108, 68398967956430765712, 1024826569020715088508, 15405900278361291658896
OFFSET
1,2
FORMULA
a(n) = A054474(n)/4.
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
CROSSREFS
Cf. A054474.
Sequence in context: A371787 A222508 A220841 * A343425 A054766 A369216
KEYWORD
nonn,walk
AUTHOR
Hugo Pfoertner, Dec 05 2023
STATUS
approved