A026591 - OEIS

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