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Search: id:A073386
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| A073386 |
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Ninth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. |
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+0
1
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| 1, 20, 230, 1980, 14135, 88264, 497860, 2591160, 12630475, 58295380, 256887774, 1087825180, 4449607565, 17654254880, 68177369040, 257006941664, 948023601910, 3428968838680, 12182953719860
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For a(n) in terms of U(n+1) and U(n) with U(n) := A000129(n+1) see the row polynomials of triangles A058402 and A058403 and the comment there.
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FORMULA
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a(n)=sum(b(k)*c(n-k), k=0..n) with b(k) := A000129(k+1) and c(k) := A073385(k).
a(n)=sum((2^n)*binomial(n-k+9, 9)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
G.f.: 1/(1-(2+x)*x)^10.
a(n)=F'''''''''(n+10, 2)/9!, that is, 1/9! times the 9th derivative of the (n+10)th Fibonacci polynomial evaluated at x=2. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006
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CROSSREFS
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Tenth (m=9) column of triangle A054456.
Sequence in context: A112503 A007160 A023018 this_sequence A022648 A004315 A074334
Adjacent sequences: A073383 A073384 A073385 this_sequence A073387 A073388 A073389
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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