A026591 - OEIS

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A026591

a(n) = T(2*n, n-1), where T is given by A026584.

1, 2, 9, 38, 140, 701, 2534, 13294, 48369, 258430, 947694, 5114572, 18872399, 102539204, 380143356, 2075658454, 7723000261, 42330184638, 157951859953, 868376395790, 3247811317907, 17899895038348, 67075896452000, 370442993383238, 1390392820937920, 7692166179956366, 28910883325637649, 160184255555687056

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OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A026584(2*n, n-1).

MATHEMATICA

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 *)

a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n, n-1]];

Table[a[n], {n, 1, 40}] (* G. C. Greubel, Dec 13 2021 *)

PROG

(Sage)

@CachedFunction

def T(n, k): # T = A026584

if (k==0 or k==2*n): return 1

elif (k==1 or k==2*n-1): return (n//2)

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)

[T(2*n, n-1) for n in (1..40)] # G. C. Greubel, Dec 13 2021

CROSSREFS