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%I #4 Apr 04 2024 10:31:48
%S 1,2,11,113,1732,35509,914213,28372686,1031486867,43009596241,
%T 2023804597256,106098215717113,6133027601141401,387563995785510010,
%U 26581805841852520619,1966679438751901515329,156133093759166939659212,13239463980230688450540781,1194277034550296812912993853
%N Row sums of triangle A370262.
%F a(n) = Sum_{k = 0..n} binomial(n+k, n-k)/(2*k+1) * (2*n+1)^k
%F a(n)^2 = 2/(2*n + 1)^3 * (T(2*n+1, n+3/2) - 1), where T(n, x) denotes the n-th Chebyshev polynomial of the first kind.
%p seq(add(binomial(n+k, n-k)/(2*k+1) * (2*n+1)^k, k = 0..n), n = 0..20);
%Y Cf. A370262.
%K nonn,easy
%O 0,2
%A _Peter Bala_, Apr 03 2024
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