A027080 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027052.

2, 15, 100, 757, 5902, 46907, 377520, 3065809, 25078650, 206416795, 1708129244, 14202265321, 118585167502, 993915161547, 8358970631568, 70518298143329, 596590060985546, 5060232622624651, 43022268222676124, 366575545244139845, 3129747701356459022, 26771150349554898415

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..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+2), k=0..2*n-2), n=2..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+2], {k, 0, 2*n-2}], {n,2,30}] (* 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+2) for k in (0..2*n-2)) for n in (2..30)] # G. C. Greubel, Nov 07 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019