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

0,2

Links

Table of n, a(n) for n=0..20.

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);

Prog

(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

Crossrefs

Cf. A377657.

Sequence in context: A358609 A364791 A020122 * A327426 A086554 A213324

Adjacent sequences: A377655 A377656 A377657 * A377659 A377661 A377662

Keyword

nonn

Author

Peter Luschny, Nov 11 2024

Status

approved