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

%I A366924 #14 Jan 28 2025 06:52:14
%S A366924 1,5,44,469,5516,68892,896016,11998869,164259308,2287663804,
%T A366924 32303714576,461352451292,6651528522256,96669999247184,
%U A366924 1414652852290752,20825721430968213,308191001159544876,4581880220433822108,68398967956430765712,1024826569020715088508,15405900278361291658896
%N A366924 Number of 2n-step walks on square lattice starting and ending at the origin with first step north and avoiding early returns.
%F A366924 a(n) = A054474(n)/4.
%p A366924 b:= proc(n) b(n):= binomial(2*n, n)^2 end:
%p A366924 a:= proc(n) option remember;
%p A366924       b(n)/4-add(a(n-i)*b(i), i=1..n-1)
%p A366924     end:
%p A366924 seq(a(n), n=1..21);  # _Alois P. Heinz_, Dec 05 2023
%t A366924 b[n_] := b[n] = Binomial[2*n, n]^2;
%t A366924 a[n_] := a[n] = b[n]/4 - Sum[a[n-i]*b[i], {i, 1, n-1}];
%t A366924 Table[a[n], {n, 1, 21}] (* _Jean-François Alcover_, Jan 28 2025, after _Alois P. Heinz_ *)
%Y A366924 Cf. A054474.
%K A366924 nonn,walk
%O A366924 1,2
%A A366924 _Hugo Pfoertner_, Dec 05 2023