A027079 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027052.

0, 4, 24, 160, 1136, 8420, 64224, 499984, 3952928, 31634724, 255682432, 2083562368, 17097573344, 141143273396, 1171240794072, 9763809318912, 81724975129664, 686539343850164

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( add(T(n,k)*T(n,k+1), k=0..2*n-1), n=1..30); # G. C. Greubel, Nov 07 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}], {n,30}] (* G. C. Greubel, Nov 07 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n,k)*T(n,k+1) for k in (0..2*n-1)) for n in (1..30)] # G. C. Greubel, Nov 07 2019