A026772 - OEIS

%I #7 Nov 01 2019 22:22:48

%S 1,10,71,444,2616,14938,83821,465654,2572166,14164320,77886902,

%T 428113940,2353823912,12950837432,71326701751,393289209772,

%U 2171308560036,12003376308370,66445540183348,368304502202306,2044177115127750

%N a(n) = T(2n, n-2), T given by A026769.

%H G. C. Greubel, <a href="/A026772/b026772.txt">Table of n, a(n) for n = 2..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 n=2 and k=1 then 2;

%p    elif 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, n-2), n=2..30); # _G. C. Greubel_, Nov 01 2019

%t T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[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[2*n, n-2], {n,2,30}] (* _G. C. Greubel_, Nov 01 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

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

%o     elif (n==2 and k==1): return 2

%o     elif (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, n-2) for n in (2..30)] # _G. C. Greubel_, Nov 01 2019

%Y Cf. A026769, A026770, A026771, A026773, A026774, A026775, A026776, A026777, A026778, A026779.

%K nonn

%O 2,2

%A _Clark Kimberling_