A371697 Row sums of triangle A370262.

1, 2, 11, 113, 1732, 35509, 914213, 28372686, 1031486867, 43009596241, 2023804597256, 106098215717113, 6133027601141401, 387563995785510010, 26581805841852520619, 1966679438751901515329, 156133093759166939659212, 13239463980230688450540781, 1194277034550296812912993853

Offset: 0

Author

Peter Bala, Apr 03 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A370262.

Programs

Maple

seq(add(binomial(n+k, n-k)/(2*k+1) * (2*n+1)^k, k = 0..n), n = 0..20);

Formula

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

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.