A027262 a(n) = self-convolution of row n of array T given by A026519.

1, 3, 8, 58, 196, 1608, 5774, 48924, 180772, 1553940, 5837908, 50618184, 192239854, 1676640462, 6416509142, 56201554888, 216309089956, 1900789437276, 7347943049432, 64734185205960, 251119894730596, 2216888144737508, 8624336421678788, 76265067399850848, 297394187356638766

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026532, A026533, A026534, A027263, A027264, A027265, A027266.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n,k]*T[n,2*n-k], {k,0,2*n}] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 21 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026519
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n,k)*T(n,2*n-k) for k in (0..2*n) )
[a(n) for n in (0..40)] # G. C. Greubel, Dec 22 2021

Formula

a(n) = Sum_{k=0..2*n} A026519(n, k)*A026519(n, 2*n-k).

Extensions

More terms from Sean A. Irvine, Oct 26 2019