A027264 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A026519.

5, 40, 150, 1279, 4797, 41462, 156900, 1365014, 5205950, 45501743, 174609162, 1531614109, 5906040623, 51952990090, 201114700568, 1773182087440, 6885880226784, 60825762159338, 236826459554380, 2095280066101886, 8175978023317170, 72432026278468535, 283166067626865540

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026532, A026533, A026534, A027262, A027263, A027265, A027266.

Programs

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+2], {k, 0, 2*n-2}] ];
Table[a[n], {n, 2, 40}] (* G. C. Greubel, Dec 21 2021 *)

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+2) for k in (0..2*n-2) )
[a(n) for n in (2..40)] # G. C. Greubel, Dec 21 2021

Formula

a(n) = Sum_{k=0..2n-2} A026519(n,k) * A026519(n,k+2).

Extensions

More terms from Sean A. Irvine, Oct 26 2019