A027282 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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