A027072 a(n) = self-convolution of row n of array T given by A027052.

1, 2, 3, 12, 53, 222, 899, 3540, 13657, 51882, 194727, 723760, 2668453, 9771870, 35577935, 128887616, 464885073, 1670362418, 5981289455, 21352860808, 76020123293, 269977176422, 956644165503, 3382864303648, 11940005836537

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..2*n} T(n,k)*T(n,2*n-k), where T = A027052. - G. C. Greubel, Nov 06 2019

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( add(T(n, k)*T(n, 2*n-k), k=0..2*n), n=0..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n, k]*T[n, 2*n-k], {k, 0, 2*n}], {n, 0, 30}] (* G. C. Greubel, Nov 06 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n, k)*T(n, 2*n-k) for k in (0..2*n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A307956 A358716 A002638 * A083746 A025231 A366454

Adjacent sequences: A027069 A027070 A027071 * A027073 A027074 A027075

Keyword

nonn

Author

Clark Kimberling

Status

approved