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 A364371 G.f. satisfies A(x) = (1 + x) * (1 - x*A(x)^2). 4
 1, 0, -1, 2, -2, -1, 9, -20, 20, 24, -150, 327, -293, -599, 3097, -6452, 4854, 15878, -71252, 140112, -81328, -437346, 1746254, -3214989, 1223971, 12345295, -44552833, 76242173, -11292089, -354175849, 1167638037, -1842585992, -233903034, 10273377388, -31169512310 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..34. FORMULA G.f.: A(x) = 2*(1 + x) / (1 + sqrt(1+4*x*(1 + x)^2)). a(n) = Sum_{k=0..n} (-1)^k * binomial(2*k+1,k) * binomial(2*k+1,n-k) / (2*k+1). D-finite with recurrence (n+1)*a(n) +(5*n-1)*a(n-1) +6*(2*n-3)*a(n-2) +6*(2*n-5)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Jul 25 2023 MAPLE A364371 := proc(n) add((-1)^k* binomial(2*k+1, k) * binomial(2*k+1, n-k)/(2*k+1), k=0..n) ; end proc: seq(A364371(n), n=0..70); # R. J. Mathar, Jul 25 2023 PROG (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*k+1, k)*binomial(2*k+1, n-k)/(2*k+1)); CROSSREFS Cf. A364372, A364373. Cf. A073157. Sequence in context: A175714 A291082 A295855 * A285068 A306149 A134896 Adjacent sequences: A364368 A364369 A364370 * A364372 A364373 A364374 KEYWORD sign AUTHOR Seiichi Manyama, Jul 20 2023 STATUS approved

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Last modified August 6 02:44 EDT 2024. Contains 374957 sequences. (Running on oeis4.)