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

2,1

Links

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

Formula

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

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 *)

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

Crossrefs

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

Sequence in context: A244725 A319098 A209346 * A025214 A222613 A272226

Adjacent sequences: A027261 A027262 A027263 * A027265 A027266 A027267

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved