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A156566
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a(2n+2) = 9*a(2n+1), a(2n+1) = 9*a(2n) - 8^n*A000108(n), a(0)=1.
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3
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1, 8, 72, 640, 5760, 51712, 465408, 4186112, 37675008, 339017728, 3051159552, 27459059712, 247131537408, 2224149233664, 20017343102976, 180155188248576, 1621396694237184, 14592546256715776, 131332916310441984
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 8^C(n+1,2).
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A120730(n,k)*8^k.
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MATHEMATICA
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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 *)
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 *)
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PROG
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(SageMath)
if (n==0): return 1
elif (n%2==1): return 9*a(n-1) - 8^((n-1)/2)*catalan_number((n-1)/2)
else: return 9*a(n-1)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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