A027270 - OEIS

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

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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