A027282 a(n) = self-convolution of row n of array T given by A026584.

1, 2, 8, 40, 222, 1296, 7770, 47324, 291260, 1806220, 11266718, 70609316, 444231564, 2803975860, 17748069294, 112609964308, 716010467122, 4561107325336, 29103104031990, 185973253609716, 1189979068401564, 7623432519587692, 48891854980251090, 313874287333373820

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

Bisection of A026585.

Links

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

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027283, A027284, A027285, A027286.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Sum[T[n, k]*T[n, 2*n-k], {k,0,2*n}];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 15 2021 *)

Sage

@CachedFunction
def T(n, k):  # T = A026584
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n//2)
    else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
@CachedFunction
def A027282(n): return sum(T(n,j)*T(n, 2*n-j) for j in (0..2*n))
[A027282(n) for n in (0..40)] # G. C. Greubel, Dec 15 2021

Formula

a(n) = Sum_{k=0..2*n} A026584(n, k)*A026584(n, 2*n-k).

Extensions

More terms from Sean A. Irvine, Oct 26 2019