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A054441
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Convolution of (shifted) A026671 with A000984 (central binomial coefficients of even order).
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2
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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
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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G.f.: cbie(x)*x/(-x+1/cbie(x)), with cbie(x)=1/sqrt(1-4*x) = g.f. for A000984.
a(n) = sum(A026671(k-1)*binomial(2*(n-k), n-k), k=0..n), with A026671(-1) := 0. a(n)= A026671(n)-binomial(2*n, n).
a(n) = sum(a(k-1)*binomial(2*(n-k), n-k), k=1..n) + 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
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MATHEMATICA
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Table[SeriesCoefficient[x/((-x+Sqrt[1-4*x])*Sqrt[1-4*x]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 09 2012 *)
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PROG
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(PARI) x='x+O('x^66); concat([0], Vec(x/((-x+sqrt(1-4*x))*sqrt(1-4*x)))) \\ Joerg Arndt, May 06 2013
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CROSSREFS
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Cf. A026671, A000984.
Sequence in context: A113443 A124999 A120902 * A102285 A218985 A129162
Adjacent sequences: A054438 A054439 A054440 * A054442 A054443 A054444
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang Mar 21 2000
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STATUS
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approved
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