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 A337467 Expansion of sqrt(2 / ( (1-2*x+49*x^2) * (1-7*x+sqrt(1-2*x+49*x^2)) )). 2
 1, 3, -21, -139, 531, 6489, -9723, -292293, -135117, 12514313, 29905809, -501239553, -2310673379, 18245192679, 140574917259, -562805403867, -7557237645741, 11275709877369, 371974318253601, 201852054629631, -16932135947326551, -42530838930147813, 709138646702505999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k=0..n} (-3)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k). a(0) = 1, a(1) = 3 and n * (2*n+1) * (4*n-3) * a(n) = (4*n-1) * (4*n^2-2*n+1) * a(n-1) - 49 * (n-1) * (2*n-1) * (4*n+1) * a(n-2) for n > 1. - Seiichi Manyama, Aug 29 2020 MATHEMATICA a[n_] := Sum[(-3)^(n-k) * Binomial[2*k, k] * Binomial[2*n+1, 2*k], {k, 0, n}]; Array[a, 23, 0] (* Amiram Eldar, Apr 29 2021 *) PROG (PARI) N=40; x='x+O('x^N); Vec(sqrt(2/((1-2*x+49*x^2)*(1-7*x+sqrt(1-2*x+49*x^2))))) (PARI) {a(n) = sum(k=0, n, (-3)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))} CROSSREFS Column k=3 of A337464. Cf. A245927, A337422. Sequence in context: A346935 A137969 A303349 * A318041 A054419 A228115 Adjacent sequences:  A337464 A337465 A337466 * A337468 A337469 A337470 KEYWORD sign AUTHOR Seiichi Manyama, Aug 28 2020 STATUS approved

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Last modified August 15 09:19 EDT 2022. Contains 356135 sequences. (Running on oeis4.)