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A027263
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A026519.
21
2, 6, 52, 180, 1516, 5502, 46936, 174456, 1504432, 5673140, 49288856, 187675644, 1639174304, 6284986554, 55108565584, 212408191568, 1868067054968, 7229648901024, 63734526307552, 247468885359240, 2185849699156352, 8510025522045036, 75288454939134992, 293772371437293720
OFFSET
1,1
LINKS
FORMULA
a(n) = Sum_{k=0..2n-1} A026519(n,k) * A026519(n,k+1).
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/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 = A026519 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}] ];
Table[a[n], {n, 40}] (* G. C. Greubel, Dec 21 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026519
if (k<0 or k>2*n): return 0
elif (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+1)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n, k)*T(n, k+1) for k in (0..2*n-1) )
[a(n) for n in (1..40)] # G. C. Greubel, Dec 21 2021
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 26 2019
STATUS
approved