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A133309
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(1/n)*Sum[i=0..n-1,C(n,i)*C(n,i-1)*8^i*9^(n-i)], a(0)=1.
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4
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1, 9, 153, 3249, 77265, 1968633, 52546473, 1450365921, 41058670113, 1185580310121, 34783088255289, 1033907690362257, 31070005849929969, 942384250116160857, 28812102048874578249, 887007207177728561601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ninth column of array A103209 .
The Hankel transform of this sequence is 72^C(n+1,2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
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FORMULA
| G.f.: z[1-z-(z^2-34z+1)^(1/2)]/(16z). a(n) = Sum_{k, 0<=k<=n}A088617(n,k)*8^k . a(n) = Sum_{k, 0<=k<=n} A060693(n,k)*8^(n-k). a(n) = Sum_{k, 0<=k<=n}C(n+k, 2k)8^k*C(k), C(n) given by A000108 .
a(0)=1, a(n)=a(n-1)+8*Sum_{k, 0<=k<=n-1}a(k)*a(n-1-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
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MATHEMATICA
| Rest@ Rest@ CoefficientList[ Series[x(1 - x - Sqrt[x^2 - 34x + 1])/16, {x, 0, 18}], x] - Robert G. Wilson v (rgwv(at)rgwv.com), Oct 19 2007
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CROSSREFS
| Cf. A000108, A060693, A103209, A103210, A103211.
Sequence in context: A169958 A012017 A130980 * A151835 A113391 A045755
Adjacent sequences: A133306 A133307 A133308 * A133310 A133311 A133312
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2007
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 19 2007
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