A027215 Self-convolution of row n of array T given by A026736.

1, 2, 6, 20, 78, 282, 1187, 4428, 19175, 72820, 319493, 1227712, 5424359, 21018514, 93252862, 363563668, 1617342486, 6334904252, 28232695584, 110982722888, 495257577162

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026736.

Programs

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([0..20], n-> Sum([0..n], k-> T(n, k)*T(n,n-k) )); # G. C. Greubel, Jul 19 2019

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, n-k], {k,0,n}], {n,0,40}] (* G. C. Greubel, Jul 19 2019 *)

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(21, n, n--; sum(k=0, n, T(n, k)*T(n,n-k)) ) \\ G. C. Greubel, Jul 19 2019

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    if (k==n-1): return n
    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,n-k) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 19 2019