A026762 - OEIS

%I #10 Nov 01 2019 03:55:06

%S 1,4,16,66,279,1201,5242,23133,103015,462269,2088146,9487405,43328580,

%T 198798447,915950385,4236322720,19661850045,91549502656,427539667095,

%U 2002120576312,9399659155395,44234927105888,208631813215116

%N a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.

%H G. C. Greubel, <a href="/A026762/b026762.txt">Table of n, a(n) for n = 1..500</a>

%p T:= proc(n,k) option remember;

%p    if n<0 then 0;

%p    elif k=0 or k = n then 1;

%p    elif type(n,'odd') and k <= (n-1)/2 then

%p         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;

%p    else

%p        procname(n-1,k-1)+procname(n-1,k) ;

%p    end if ;

%p end proc;

%p seq(T(2*n-1,n-1), n=1..30); # _G. C. Greubel_, Oct 31 2019

%t T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && k<=(n - 1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]; Table[T[2n-1, n-1], {n, 0, 30}] (* _G. C. Greubel_, Oct 31 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o     if (n<0): return 0

%o     elif (k==0 or k==n): return 1

%o     elif (mod(n,2)==1 and k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)

%o     else: return T(n-1,k-1) + T(n-1,k)

%o [T(2*n-1, n-1) for n in (1..30)] # _G. C. Greubel_, Oct 31 2019

%Y Cf. A026747, A026758, A026759, A026760, A026761, A026763, A026764, A026765, A026766, A026767, A026768.

%K nonn

%O 1,2

%A _Clark Kimberling_