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 A054441 Convolution of (shifted) A026671 with A000984 (central binomial coefficients of even order). 4
 0, 1, 5, 23, 103, 455, 1993, 8679, 37633, 162643, 701075, 3015563, 12948083, 55513327, 237705547, 1016736115, 4344766607, 18550920063, 79149527249, 337482635279, 1438155203665, 6125448713739, 26077796587441, 110974892937943, 472081467302933, 2007534192877275, 8534465842495133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: cbie(x)*x/(-x+1/cbie(x)), with cbie(x)=1/sqrt(1-4*x) = g.f. for A000984. a(n) = Sum_{k=0..n} A026671(k-1)*binomial(2*(n-k), n-k), with A026671(-1):= 0. a(n) = A026671(n) - binomial(2*n, n). a(n) = Sum_{k=1..n} a(k-1)*binomial(2*(n-k), n-k) + 4^(n-1), n >= 1. Recurrence: (n-2)*a(n) = 2*(4*n-9)*a(n-1) - (15*n-38)*a(n-2) - 2*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 09 2012 a(n) ~ (sqrt(5)+2)^n/sqrt(5). - Vaclav Kotesovec, Oct 09 2012 a(n) = Sum_{k=1..n} binomial(2*n,n-k)*F(k), where F denotes a Fibonacci number (A000045). - Vladimir Kruchinin, Mar 19 2016 MATHEMATICA Table[SeriesCoefficient[x/((-x+Sqrt[1-4*x])*Sqrt[1-4*x]), {x, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 09 2012 *) PROG (PARI) x='x+O('x^66); concat([0], Vec(x/((-x+sqrt(1-4*x))*sqrt(1-4*x)))) \\ Joerg Arndt, May 06 2013 (Maxima) a(n):=sum(fib(k)*binomial(2*n, n-k), k, 1, n); /* Vladimir Kruchinin, Mar 19 2016 */ (MAGMA) [(&+[Binomial(2*n, n-k)*Fibonacci(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jul 15 2019 (Sage) [sum(binomial(2*n, n-k)*fibonacci(k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jul 15 2019 (GAP) List([0..30], n-> Sum([0..n], k-> Binomial(2*n, n-k)*Fibonacci(k) )); # G. C. Greubel, Jul 15 2019 CROSSREFS Cf. A000045, A000984, A026671. Sequence in context: A124999 A258431 A120902 * A289803 A102285 A218985 Adjacent sequences:  A054438 A054439 A054440 * A054442 A054443 A054444 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Mar 21 2000 STATUS approved

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Last modified July 26 15:49 EDT 2021. Contains 346294 sequences. (Running on oeis4.)