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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..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, n-k], {k, 0, n}], {n, 0, 40}] (* 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(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
(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

Crossrefs

Cf. A026736.

Sequence in context: A148484 A148485 A287424 * A150177 A150178 A150179

Adjacent sequences: A027212 A027213 A027214 * A027216 A027217 A027218

Keyword

nonn

Author

Clark Kimberling

Status

approved