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A336712 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} 2^(n-k) * binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.

%I A336712 #13 Aug 03 2020 10:27:55
%S A336712 1,1,4,30,364,6502,158034,4921112,187897728,8519286854,447829041358,
%T A336712 26796275824186,1798936842255128,133933302810144684,
%U A336712 10953460639289615412,976226180855018504472,94181146038753255120480,9778885058353578446996934,1087326670244362420301889926
%N A336712 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} 2^(n-k) * binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.
%H A336712 Seiichi Manyama, <a href="/A336712/b336712.txt">Table of n, a(n) for n = 0..339</a>
%t A336712 a[0] = 1; a[n_] := Sum[2^(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 A336712 (PARI) {a(n) = if(n==0, 1, sum(k=1, n, 2^(n-k)*binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)}
%Y A336712 Main diagonal of A336707.
%Y A336712 Cf. A336578, A335871, A336713, A336714.
%K A336712 nonn
%O A336712 0,3
%A A336712 _Seiichi Manyama_, Aug 01 2020