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A336728 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.

%I A336728 #20 Aug 03 2020 08:52:33
%S A336728 1,1,-1,1,9,-174,2575,-38219,588833,-9274418,141253551,-1739881142,
%T A336728 -753419447,1379742127908,-83720072007585,4059017293956301,
%U A336728 -184613801568558975,8254420480122200214,-369177108304219471457,16608406418618863804990,-750673988803431836351799
%N A336728 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.
%H A336728 Seiichi Manyama, <a href="/A336728/b336728.txt">Table of n, a(n) for n = 0..387</a>
%F A336728 a(n) = Sum_{k=0..n} (-n)^k * (n+1)^(n-k) * binomial(n,k) * binomial(n+k,n)/(k+1).
%t A336728 a[0] = 1; a[n_] := Sum[(-n)^(n - k) * Binomial[n, k] * Binomial[n , k - 1], {k, 1, n}] / n; Array[a, 21, 0] (* _Amiram Eldar_, Aug 02 2020 *)
%o A336728 (PARI) {a(n) = if(n==0, 1, sum(k=1, n, (-n)^(n-k)*binomial(n, k)*binomial(n, k-1))/n)}
%o A336728 (PARI) {a(n) = sum(k=0, n, (-n)^k*(n+1)^(n-k)*binomial(n, k)*binomial(n+k, n)/(k+1))}
%Y A336728 Main diagonal of A336727.
%Y A336728 Cf. A242369, A307885, A336713, A336714.
%K A336728 sign
%O A336728 0,5
%A A336728 _Seiichi Manyama_, Aug 02 2020