A377658 a(n) = Sum_{k=0 .. n} Sum_{j=0 .. k} tan(j*Pi/(1 + 2*k))^(2*(n - k)). Antidiagonal sums of A377657.

1, 2, 6, 23, 143, 1344, 16476, 248509, 4519021, 97094158, 2419043330, 68973522675, 2228418011291, 80844520830828, 3266496719516152, 145973848760893369, 7172279845906943513, 385419654638220638810, 22543794177677289243966, 1429137150185034529444879, 97815341290407924477479399

Offset: 0

Author

Peter Luschny, Nov 11 2024

Keywords

• nonn

Crossrefs

Cf. A377657.

Programs

Maple

a := n -> add(add(tan(j*Pi/(1 + 2*k))^(2*(n - k)), j = 0..k), k = 0..n):
seq(round(evalf(a(n), 64)), n = 0..20);

PARI

a(n) = { sum(k=0, n, trace(matcompanion(sum(m=0, k, x^m*binomial(2*k+1, 2*(k-m))*(-1)^(m+1)))^(n-k))+((n-k)==0)) } \\ Thomas Scheuerle, Nov 11 2024