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A027274
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A026552.
18
10, 40, 342, 1279, 11016, 41462, 359530, 1365014, 11899516, 45501743, 398306769, 1531614109, 13450930624, 51952990090, 457449811458, 1773182087440, 15646091896400, 60825762159338, 537651887201990, 2095280066101886, 18547910336883720, 72432026278468535
OFFSET
2,1
LINKS
FORMULA
a(n) = Sum_{k=0..2*n-2} A026552(n,k) * A026552(n,k+2).
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+2], {k, 0, 2*n-2}]];
Table[a[n], {n, 2, 40}] (* G. C. Greubel, Dec 18 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026552
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+2)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n, k)*T(n, k+2) for k in (0..2*n-2) )
[a(n) for n in (2..40)] # G. C. Greubel, Dec 18 2021
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 26 2019
STATUS
approved