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%I #15 Aug 03 2020 10:28:13
%S 1,1,1,6,76,1447,37206,1212194,47975271,2238595055,120453255172,
%T 7347494056729,501273291296174,37833413358907566,3130557361463956074,
%U 281854137496597897755,27433898122963009937892,2870816347095046227070383,321430790732030793454519088
%N a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.
%H Seiichi Manyama, <a href="/A336713/b336713.txt">Table of n, a(n) for n = 0..339</a>
%t a[0] = 1; a[n_] := Sum[(-1)^(n - k) * 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, (-1)^(n-k)*binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)}
%Y Main diagonal of A336708.
%Y Cf. A336578, A335871, A336712, A336714.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Aug 01 2020
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