A027217 a(n) = Sum_{k=0..n-2} T(n,k)*T(n,k+2), T given by A026736.

1, 6, 32, 136, 640, 2593, 11860, 47532, 215531, 861334, 3893621, 15549166, 70199065, 280316029, 1264697307, 5050617474, 22776900816, 90972831448, 410117333080

Offset

2,2

Links

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

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]]; Table[Sum[T[n, k]*T[n, k+2], {k, 0, n-2}], {n, 2, 30}] (* G. C. Greubel, Jul 19 2019 *)

Prog

(PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
vector(20, n, n++; sum(k=0, n-2, T(n, k)*T(n, k+2)) ) \\ G. C. Greubel, Jul 19 2019
(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1)
+ T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n, k)*T(n, k+2) for k in (0..n-2)) for n in (2..30)] # G. C. Greubel, Jul 19 2019
(GAP)
T:= function(n, k)
    if k=0 or k=n then return 1;
    elif k=n-1 then return n;
    elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
    else return T(n-1, k-1) + T(n-1, k);
    fi;
  end;
List([2..20], n-> Sum([0..n-2], k-> T(n, k)*T(n, k+2) )); # G. C. Greubel, Jul 19 2019

Crossrefs

Cf. A026736.

Sequence in context: A130410 A202807 A203324 * A245128 A121333 A243026

Adjacent sequences: A027214 A027215 A027216 * A027218 A027219 A027220

Keyword

nonn

Author

Clark Kimberling

Status

approved