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 A365879 Expansion of (1/x) * Series_Reversion( x*(1+x)^3*(1-x)^5 ). 5
 1, 2, 10, 54, 332, 2162, 14734, 103630, 746857, 5486206, 40926152, 309202686, 2361065920, 18192978966, 141280871840, 1104603758526, 8687878404289, 68692224882620, 545681467048132, 4353096328518810, 34858239962177764, 280095777427596008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. Index entries for reversions of series FORMULA a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(3*n+k+2,k) * binomial(6*n-k+4,n-k). a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(3*n-2*k+1,n-2*k). - Seiichi Manyama, Jan 18 2024 a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^5 )^(n+1). - Seiichi Manyama, Feb 16 2024 PROG (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*n+k+2, k)*binomial(6*n-k+4, n-k))/(n+1); (SageMath) def A365879(n): h = binomial(6*n + 4, n) * hypergeometric([-n, 3*(n + 1)], [-6 * n - 4], -1) / (n + 1) return simplify(h) print([A365879(n) for n in range(22)]) # Peter Luschny, Sep 21 2023 CROSSREFS Cf. A365753, A365856, A365880. Cf. A365878, A368079. Cf. A370270. Sequence in context: A272178 A152395 A369263 * A202365 A330620 A268556 Adjacent sequences: A365876 A365877 A365878 * A365880 A365881 A365882 KEYWORD nonn,changed AUTHOR Seiichi Manyama, Sep 21 2023 STATUS approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)