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 A331793 Expansion of ((1 - 5*x)/sqrt(1 - 10*x + 9*x^2) - 1)/(8*x^2). 2
 1, 10, 87, 740, 6285, 53550, 458115, 3934600, 33913881, 293244050, 2542684463, 22101612780, 192530903461, 1680415209270, 14692052109915, 128653303453200, 1128147127156785, 9905115333850650, 87066787614156807, 766127762539955700, 6747880819438628541 (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) = (2/(n+2)) * A331516(n) = Sum_{k=0..n} 4^k * binomial(n+1,k) * binomial(n+1,k+1). n * (n+2) * a(n) = (n+1) * (5 * (2*n+1) * a(n-1) - 9 * n * a(n-2)) for n>1. a(n) ~ 3^(2*n + 3) / (2^(5/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jan 26 2020 MATHEMATICA a[n_] := Sum[4^k * Binomial[n + 1, k] * Binomial[n + 1, k + 1], {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, May 05 2021 *) PROG (PARI) N=20; x='x+O('x^N); Vec(((1-5*x)/sqrt(1-10*x+9*x^2)-1)/(8*x^2)) (PARI) {a(n) = sum(k=0, n, 4^k*binomial(n+1, k)*binomial(n+1, k+1))} CROSSREFS Column 5 of A331791. Cf. A331516. Sequence in context: A218894 A251193 A198858 * A121115 A292998 A114648 Adjacent sequences:  A331790 A331791 A331792 * A331794 A331795 A331796 KEYWORD nonn AUTHOR Seiichi Manyama, Jan 26 2020 STATUS approved

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Last modified May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)