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Search: id:A073385
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| A073385 |
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Eighth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. |
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+0
2
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| 1, 18, 189, 1500, 9945, 58014, 307197, 1507176, 6950295, 30443270, 127666539, 515754252, 2017069431, 7667214570, 28419251715, 102997948704, 365832349542, 1275914693196, 4376992440590
(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) := A073384(k).
a(n)=sum((2^n)*binomial(n-k+8, 8)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
G.f.: 1/(1-(2+x)*x)^9.
a(n)=F''''''''(n+9, 2)/8!, that is, 1/8! times the 8th derivative of the (n+9)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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Ninth (m=8) column of triangle A054456.
Sequence in context: A036396 A036394 A023016 this_sequence A036219 A022646 A004314
Adjacent sequences: A073382 A073383 A073384 this_sequence A073386 A073387 A073388
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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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