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 A026674 a(n) = T(2n-1,n-1) = T(2n,n+1), T given by A026725. 10
 1, 4, 16, 65, 267, 1105, 4597, 19196, 80380, 337284, 1417582, 5965622, 25130844, 105954110, 447015744, 1886996681, 7969339643, 33670068133, 142301618265, 601586916703, 2543852427847, 10759094481491, 45513214057191, 192560373660245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Rob Arthan, Comments on A026674, A026725, A026670 Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5. FORMULA G.f.: 1/2*[(1-x)/(sqrt(1-4x)-x)-1] (conjectured). - Ralf Stephan, Feb 05 2004 G.f.: x*c(x)^3/(1-x*c(x)^3) = (1-5x-(1-x)sqrt(1-4x))/(2(x^2+4x-1)), c(x) the g.f. of A000108. - Paul Barry, Mar 19 2007 a(n) = the upper left term in M^n, where M is the following infinite square production matrix: 1,  1, 0, 0, 0, 0, 0,... 3,  1, 1, 0, 0, 0, 0,... 6,  1, 1, 1, 0, 0, 0,... 10, 1, 1, 1, 1, 0, 0,... 15, 1, 1, 1, 1, 1, 0,... 21, 1, 1, 1, 1, 1, 1,... ... - Gary W. Adamson, Jul 11 2011 Conjecture: n*a(n) +(-9*n+8)*a(n-1) +23*(n-2)*a(n-2) +(-11*n+48)*a(n-3) +2*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Nov 26 2012 a(n) = 1/n*Sum_{k=1..n} k*binomial(2*n,n-k)*Sum_{i=0..k/2} binomial(k-i,i). - Vladimir Kruchinin, Apr 28 2016 MAPLE a := n -> add(binomial(2*n, n+k)*combinat:-fibonacci(1+k)*(k/n), k=1..n): seq(a(n), n=1..24); # Peter Luschny, Apr 28 2016 MATHEMATICA a[n_] := Sum[Binomial[2n, n+k] Fibonacci[k+1] k/n, {k, 1, n}]; Array[a, 24] (* Jean-François Alcover, Jun 21 2018, after Peter Luschny *) PROG (Maxima) a(n):=sum(k*binomial(2*n, n-k)*(sum(binomial(k-i, i), i, 0, k/2)), k, 1, n)/n; /* Vladimir Kruchinin, Apr 28 2016 */ (PARI) a(n)=sum(k=1, n, k*binomial(2*n, n-k)*sum(i=0, k\2, binomial(k-i, i)))/n \\ Charles R Greathouse IV, Apr 28 2016 CROSSREFS Also a(n) = T(2n-1, n-1), T given by A026670. Sequence in context: A012781 A132820 A165201 * A099781 A026872 A081915 Adjacent sequences:  A026671 A026672 A026673 * A026675 A026676 A026677 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)