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%I #29 Aug 03 2020 10:28:16
%S 1,1,3,20,234,4159,101538,3182454,122285201,5575750271,294529785168,
%T 17697480642005,1192398100081202,89053864927236146,
%U 7302988011333915878,652439391227186881683,63077327237347821501754,6561701255914880362990927,730833849063629052249986940
%N 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.
%H Seiichi Manyama, <a href="/A335871/b335871.txt">Table of n, a(n) for n = 0..339</a>
%t 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 *)
%o (PARI) {a(n) = if(n==0, 1, sum(k=1, n, binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)}
%Y Main diagonal of A336706.
%Y Cf. A336578, A336712, A336713, A336714.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 01 2020