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 A335871 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0. 5
 1, 1, 3, 20, 234, 4159, 101538, 3182454, 122285201, 5575750271, 294529785168, 17697480642005, 1192398100081202, 89053864927236146, 7302988011333915878, 652439391227186881683, 63077327237347821501754, 6561701255914880362990927, 730833849063629052249986940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..339 MATHEMATICA a[0] = 1; a[n_] := Sum[Binomial[n, k] * Binomial[n + (n - 1)*k, k - 1], {k, 1, n}] / n; Array[a, 19, 0] (* Amiram Eldar, Aug 01 2020 *) PROG (PARI) {a(n) = if(n==0, 1, sum(k=1, n, binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)} CROSSREFS Main diagonal of A336706. Cf. A336578, A336712, A336713, A336714. Sequence in context: A194972 A294603 A240957 * A195135 A201148 A248653 Adjacent sequences: A335868 A335869 A335870 * A335872 A335873 A335874 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 01 2020 STATUS approved

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Last modified January 26 22:13 EST 2023. Contains 359836 sequences. (Running on oeis4.)