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A156577
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a(2*n+2) = 10*a(2*n+1), a(2*n+1) = 10*a(2*n) - 9^n*A000108(n), a(0) = 1.
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3
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1, 9, 90, 891, 8910, 88938, 889380, 8890155, 88901550, 888923646, 8889236460, 88889884542, 888898845420, 8888918303988, 88889183039880, 888889778505099, 8888897785050990, 88888916293698870, 888889162936988700
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 9^binomial(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) * 9^k.
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MATHEMATICA
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a[n_]:= a[n]= If[n==0, 1, If[OddQ[n], 10*a[n-1] -9^((n-1)/2)*CatalanNumber[(n-1)/2], 10*a[n-1] ]];
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PROG
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(Sage)
if (n==0): return 1
elif (n%2==1): return 10*a(n-1) - 9^((n-1)/2)*catalan_number((n-1)/2)
else: return 10*a(n-1)
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CROSSREFS
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Cf. A000108, A001405, A120730, A151162, A151254, A151281, A156195, A156273, A156361, A156362, A156566.
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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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