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

0,2

Links

Table of n, a(n) for n=0..18.

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.

Maple

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

Crossrefs

Cf. A370262.

Sequence in context: A205073 A069574 A090534 * A373795 A286869 A373645

Adjacent sequences: A371694 A371695 A371696 * A371698 A371699 A371700

Keyword

nonn,easy

Author

Peter Bala, Apr 03 2024

Status

approved