cp's OEIS Frontend

A156566 a(2n+2) = 9*a(2n+1), a(2n+1) = 9*a(2n) - 8^n*A000108(n), a(0)=1.

%I A156566 #11 May 18 2022 03:29:25
%S A156566 1,8,72,640,5760,51712,465408,4186112,37675008,339017728,3051159552,
%T A156566 27459059712,247131537408,2224149233664,20017343102976,
%U A156566 180155188248576,1621396694237184,14592546256715776,131332916310441984
%N A156566 a(2n+2) = 9*a(2n+1), a(2n+1) = 9*a(2n) - 8^n*A000108(n), a(0)=1.
%C A156566 Hankel transform is 8^C(n+1,2).
%H A156566 G. C. Greubel, <a href="/A156566/b156566.txt">Table of n, a(n) for n = 0..500</a>
%F A156566 a(n) = Sum_{k=0..n} A120730(n,k)*8^k.
%t A156566 a[0] = 1; a[1] = 8; a[2] = 72; a[n_] := a[n] = (-288*(n-2)*a[n-3] + 32*(n-2)*a[n-2] + 9*(n+1)*a[n-1])/(n+1); Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Nov 15 2016 *)
%t A156566 a[n_]:= a[n]= If[n==0, 1, If[OddQ[n], 9*a[n-1] - 8^((n-1)/2)*CatalanNumber[(n- 1)/2], 9*a[n-1]]]; Table[a[n], {n,0,30}] (* _G. C. Greubel_, May 18 2022 *)
%o A156566 (SageMath)
%o A156566 def a(n): # a = A156566
%o A156566     if (n==0): return 1
%o A156566     elif (n%2==1): return 9*a(n-1) - 8^((n-1)/2)*catalan_number((n-1)/2)
%o A156566     else: return 9*a(n-1)
%o A156566 [a(n) for n in (0..30)] # _G. C. Greubel_, May 18 2022
%Y A156566 Cf. A000108, A001405, A151162, A151254, A151281.
%Y A156566 Cf. A156195, A156270, A156361, A156362, A156577.
%Y A156566 Cf. A001018, A120730.
%K A156566 nonn
%O A156566 0,2
%A A156566 _Philippe Deléham_, Feb 10 2009