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 A073385 Eighth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. 1
 1, 18, 189, 1500, 9945, 58014, 307197, 1507176, 6950295, 30443270, 127666539, 515754252, 2017069431, 7667214570, 28419251715, 102997948704, 365832349542, 1275914693196, 4376992440590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS FORMULA 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, Jan 19 2006 MATHEMATICA CoefficientList[Series[1/(1-(2+x)x)^9, {x, 0, 20}], x] (* Harvey P. Dale, Apr 26 2017 *) PROG (Sage) taylor( mul(1/(1 - 2*x - x^2) for i in xrange(1, 10)), x, 0, 27)# Zerinvary Lajos, May 29 2009 CROSSREFS Ninth (m=8) column of triangle A054456. Sequence in context: A246059 A288836 A023016 * A036219 A022646 A268447 Adjacent sequences:  A073382 A073383 A073384 * A073386 A073387 A073388 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 02 2002 STATUS approved

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Last modified August 26 05:20 EDT 2019. Contains 326328 sequences. (Running on oeis4.)