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A386843 a(n) = Sum_{k=0..n} binomial(2*n+2,k) * binomial(2*n-k,n-k).

%I A386843 #10 Aug 05 2025 10:01:51
%S A386843 1,6,39,268,1905,13842,102123,761880,5732325,43417630,330620895,
%T A386843 2528772132,19412942809,149497184298,1154365194195,8934458916912,
%U A386843 69291946278861,538372925816886,4189702003359687,32651982699233340,254800541773725633,1990683254889381954
%N A386843 a(n) = Sum_{k=0..n} binomial(2*n+2,k) * binomial(2*n-k,n-k).
%F A386843 a(n) = [x^n] (1+x)^(2*n+2)/(1-x)^(n+1).
%F A386843 a(n) = [x^n] 1/((1-x)^2 * (1-2*x)^(n+1)).
%F A386843 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * (n-k+1) * binomial(2*n+2,k).
%F A386843 a(n) = Sum_{k=0..n} 2^k * (n-k+1) * binomial(n+k,k).
%o A386843 (PARI) a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(2*n-k, n-k));
%Y A386843 Cf. A386844, A386845.
%Y A386843 Cf. A059304, A178792.
%Y A386843 Cf. A116881.
%K A386843 nonn
%O A386843 0,2
%A A386843 _Seiichi Manyama_, Aug 05 2025