A027270 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A026536.

2, 10, 104, 420, 3786, 14826, 131264, 510576, 4508580, 17523506, 154773696, 602175444, 5323519838, 20744201142, 183586707648, 716553432640, 6348284151024, 24816637181076, 220081449149440, 861581808936200, 7647723960962932, 29978812970646870, 266322435212031984

Offset

2,1

Links

G. C. Greubel, Table of n, a(n) for n = 2..500

Formula

a(n) = Sum_{k=0..2n-3} A026536(n,k) * A026536(n,k+3).

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], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]];
Table[Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}], {n, 2, 40}] (* G. C. Greubel, Apr 12 2022 *)

Prog

(SageMath)
@CachedFunction
def T(n, k): # A026536
    if k == 0 or k == 2*n: return 1
    elif k == 1 or k == 2*n-1: return n//2
    elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
    return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
def A027270(n): return sum(T(n, k)*T(n, k+3) for k in (0..2*n-3))
[A027270(n) for n in (2..40)] # G. C. Greubel, Apr 12 2022

Crossrefs

Cf. A026536, A027267, A027268, A027269.

Sequence in context: A135058 A346672 A154256 * A304319 A005799 A208730

Adjacent sequences: A027267 A027268 A027269 * A027271 A027272 A027273

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

a(2) = 2 prepended by G. C. Greubel, Apr 12 2022

Status

approved