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%I #8 Dec 14 2021 01:45:38
%S 1,2,13,42,225,802,4235,15478,82425,304156,1634435,6064389,32819839,
%T 122244344,665162897,2484851486,13577768505,50841782786,278745377821,
%U 1045763359942,5749240499515,21603797860416,119040956286133,447922312642212,2472886893122590,9315646385012666,51514464212546865,194255376492836212
%N a(n) = T(2*n-1, n-2), where T is given by A026584.
%H G. C. Greubel, <a href="/A026594/b026594.txt">Table of n, a(n) for n = 2..1000</a>
%F a(n) = A026584(2*n-1, n-2).
%t T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k]]]]; (*T=A026584*)
%t Table[T[2*n-1, n-2], {n, 2, 40}] (* _G. C. Greubel_, Dec 13 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k): # T = A026584
%o if (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n//2)
%o else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o [T(2*n-1, n-2) for n in (2..40)] # _G. C. Greubel_, Dec 13 2021
%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
%K nonn
%O 2,2
%A _Clark Kimberling_
%E Terms a(19) onward added by _G. C. Greubel_, Dec 13 2021
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