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 A117202 Binomial transform of n*F(n). 3
 0, 1, 4, 15, 52, 170, 534, 1631, 4880, 14373, 41810, 120406, 343884, 975325, 2749852, 7713435, 21540304, 59917826, 166094370, 458998523, 1264919720, 3477182961, 9536877614, 26102772910, 71309161752, 194468551225, 529490287924 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A045925. Number of acyclic subgraphs of the wheel graph W_n (on n+1 vertices) with exactly n-1 edges. - Emil R. Vaughan, Jun 12 2007 Starting (1, 4, 15, 52, ...) = binomial transform of A136376: (1, 3, 8, 18, 37, ...). - Gary W. Adamson, Sep 03 2008 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..1000 J. Salas and A. D. Sokal, Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial, J. Stat. Phys. 135 (2009) 279-373, arXiv:0711.1738 [cond-mat.stat-mech]. Mentions this sequence. - N. J. A. Sloane, Mar 14 2014 Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1) FORMULA G.f.: x(1-2x+2x^2)/(1-3x+x^2)^2. a(n) = 6a(n-1)-11a(n-2)+6a(n-3)-a(n-4). a(n) = Sum_{k=0..n} C(n,k)*k*F(k). From Benoit Cloitre, Nov 29 2006: (Start) a(n) = Sum_[k=1..n} F(2k)*B(2n-2k)*binomial(2n,2k) where F=Fibonacci numbers and B=Bernoulli numbers; a(n) = n*F(2n-1). (End) a(n) = (2^(-1-n)*(-(-5+sqrt(5))*(3+sqrt(5))^n + (3-sqrt(5))^n*(5+sqrt(5)))*n) / 5. - Colin Barker, Feb 26 2017 MATHEMATICA Table[n Fibonacci[2n-1], {n, 0, 26}] (* or *) Table[Sum[Fibonacci[2k]*BernoulliB[2n-2k]*Binomial[2n, 2k], {k, 1, n}], {n, 0, 26}] (* or *) CoefficientList[Series[x(1-2x+2x^2)/(1-3x+x^2)^2 , {x, 0, 26}], x] (* Indranil Ghosh, Feb 26 2017 *) PROG (PARI) a(n) = n*fibonacci(2*n-1); \\ Indranil Ghosh, Feb 26 2017 (PARI) concat(0, Vec(x*(1-2*x+2*x^2) / (1-3*x+x^2)^2 + O(x^30))) \\ Colin Barker, Feb 26 2017 CROSSREFS Cf. A001519, A111262. Cf. A136376. Sequence in context: A240365 A005492 A003013 * A291011 A137213 A027853 Adjacent sequences:  A117199 A117200 A117201 * A117203 A117204 A117205 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 02 2006 STATUS approved

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Last modified June 23 23:39 EDT 2021. Contains 345403 sequences. (Running on oeis4.)