A027282 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Bisection of A026585.

LINKS

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

FORMULA

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

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 *)

PROG

(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