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 A020930 Expansion of 1/(1-4*x)^(19/2). 3
 1, 38, 798, 12236, 152950, 1651860, 15967980, 141430680, 1166803110, 9075135300, 67156001220, 476197099560, 3254013513660, 21526550936520, 138384970306200, 867212480585520, 5311676443586310, 31870058661517860 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n)=binomial(n+9, 9)*A000984(n+9)/A000984(9), where A000984 are the central binomial coefficients. - Wolfdieter Lang a(n) = ((2*n+17)*(2*n+15)*(2*n+13)*(2*n+11)*(2*n+9)*(2*n+7)*(2*n+5)*(2*n+3)*(2*n+1)/34459425)*binomial(2*n, n). - Vincenzo Librandi, Jul 05 2013 Boas-Buck recurrence: a(n) = (38/n)*Sum_{k=0..n-1} 4^(n-k-1)*a(k), n >= 1, a(0) = 1. Proof from a(n) = A046521(n+9, 9). See a comment there. - Wolfdieter Lang, Aug 10 2017 a(n) = binomial(2*(n+9),n+9)*binomial(n+9, 9)/binomial(18,9). - G. C. Greubel, Jul 21 2019 MATHEMATICA CoefficientList[Series[1/(1-4x)^(19/2), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *) PROG (MAGMA) [&*[2*n+i: i in [1..17 by 2]]*Binomial(2*n, n)/34459425: n in [0..20]]; // Vincenzo Librandi, Jul 05 2013 (PARI) vector(20, n, n--; m=n+9; binomial(2*m, m)*binomial(m, 9)/binomial(18, 9) ) \\ G. C. Greubel, Jul 21 2019 (Sage) [binomial(2*(n+9), n+9)*binomial(n+9, 9)/binomial(18, 9) for n in (0..20)] # G. C. Greubel, Jul 21 2019 (GAP) List([0..20], n-> Binomial(2*(n+9), n+9)*Binomial(n+9, 9)/Binomial(18, 9)); # G. C. Greubel, Jul 21 2019 CROSSREFS Cf. A000984, A020928, A046521 (tenth column). Sequence in context: A162392 A010990 A004420 * A104761 A270500 A268788 Adjacent sequences:  A020927 A020928 A020929 * A020931 A020932 A020933 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)