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 A365752 Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ). 9
 1, 3, 16, 103, 735, 5592, 44452, 364815, 3067558, 26290517, 228819168, 2016953848, 17968790029, 161536295244, 1463535347928, 13349907110367, 122499957767130, 1130001670577730, 10472708110616136, 97468774074103041, 910582642690819351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..20. Index entries for reversions of series FORMULA a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(5*n-k+3,n-k). a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(4*n-2*k+2,n-2*k). - Seiichi Manyama, Jan 18 2024 a(n) = (1/(n+1)) * [x^n] 1/( (1+x) * (1-x)^4 )^(n+1). - Seiichi Manyama, Feb 16 2024 PROG (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(5*n-k+3, n-k))/(n+1); (SageMath) def A365752(n): h = binomial(5*n + 3, n) * hypergeometric([-n, n + 1], [-5 * n - 3], -1) / (n + 1) return simplify(h) print([A365752(n) for n in range(21)]) # Peter Luschny, Sep 20 2023 CROSSREFS Cf. A063020, A365751, A365753. Cf. A365856, A368079. Cf. A365754, A370105. Sequence in context: A091637 A278429 A341320 * A207434 A074542 A366050 Adjacent sequences: A365749 A365750 A365751 * A365753 A365754 A365755 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 18 2023 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)