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%I #11 Aug 21 2022 11:50:12
%S 1,3,10,44,174,822,3414,16604,70600,348828,1503802,7504156,32645122,
%T 164014374,718098056,3625748104,15950473396,80839381968,356946436186,
%U 1814421022372,8035178656538,40941855317034,181746522965214,927880523400340
%N a(n) = A026681(2n,n).
%H Robert Israel, <a href="/A026682/b026682.txt">Table of n, a(n) for n = 0..1456</a>
%p T:= proc(n,k) option remember;
%p if k=0 or k=n then return 1 fi;
%p if min(k,n-k)::even then procname(n-1,k-1)+procname(n-1,k)
%p else procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k)
%p fi
%p end proc:
%p seq(T(2*n,n),n=0..40); # _Robert Israel_, Jul 16 2019
%t T[n_, k_] := T[n, k] = If[k == 0 || k == n, 1, If[EvenQ[Min[k, n-k]], T[n-1, k-1] + T[n-1, k], T[n-1, k-1] + T[n-2, k-1] + T[n-1, k]]];
%t Table[T[2n, n], {n, 0, 23}] (* _Jean-François Alcover_, Aug 21 2022, after Maple code *)
%Y Cf. A026681.
%K nonn
%O 0,2
%A _Clark Kimberling_
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