|
%I #15 Jun 18 2024 11:09:10
%S 1,1,3,5,10,17,34,60,120,217,434,798,1596,2970,5940,11154,22308,42185,
%T 84370,160446,320892,613054,1226108,2351440,4702880,9048522,18097044,
%U 34916300,69832600,135059220,270118440,523521630,1047043260,2033066025,4066132050,7908332190
%N a(n) = A026615(n, floor(n/2)).
%H G. C. Greubel, <a href="/A026621/b026621.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 2*( (49*n^2 - 287*n + 360)*a(n-1) + 2*(n-3)*(7*n-8)*(7*n-17)*a(n-2) )/((n+1)*(7*n-24)*(7*n-15)) for n > 2. - _G. C. Greubel_, Jun 13 2024
%t T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, 2*n-1, T[n -1,k-1] +T[n-1,k]]]; (* T = A026615 *)
%t Table[T[n, Floor[n/2]], {n,0,40}] (* _G. C. Greubel_, Jun 13 2024 *)
%o (Magma)
%o I:=[1,3]; [1] cat [n le 2 select I[n] else 2*((49*n^2-287*n+360 )*Self(n-1) + 2*(n-3)*(7*n-8)*(7*n-17)*Self(n-2) )/((n+1)*(7*n-24)*(7*n-15)) : n in [1..40]]; // _G. C. Greubel_, Jun 13 2024
%o (SageMath)
%o @CachedFunction
%o def T(n, k): # T = A026615
%o if k==0 or k==n: return 1
%o elif k==1 or k==n-1: return 2*n-1
%o else: return T(n-1, k-1) + T(n-1, k)
%o def A026621(n): return T(n, int(n//2))
%o [A026621(n) for n in range(41)] # _G. C. Greubel_, Jun 13 2024
%Y Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026622.
%Y Cf. A026623, A026624, A026625, A026956, A026957, A026958, A026959.
%Y Cf. A026960.
%K nonn
%O 0,3
%A _Clark Kimberling_
|
