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 A369300 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^3 ). 5
 1, 2, 7, 33, 173, 962, 5589, 33546, 206359, 1294096, 8242375, 53173095, 346724250, 2281555440, 15131448440, 101038950441, 678724811604, 4583483218340, 31098830566098, 211898222878937, 1449322361547669, 9947227335902244, 68486384818253877 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 Index entries for reversions of series FORMULA a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(3*n-3*k+1,n-3*k). a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024 PROG (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^3)/x) (PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1); CROSSREFS Cf. A369299, A369301. Cf. A369297, A369298. Cf. A369269. Sequence in context: A214954 A366237 A369269 * A055724 A301433 A054727 Adjacent sequences: A369297 A369298 A369299 * A369301 A369302 A369303 KEYWORD nonn AUTHOR Seiichi Manyama, Jan 18 2024 STATUS approved

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Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)