A393303 Denominator of Sum_{k=1..floor((n+1)/2)} binomial(n, 2*k-2) * c(k), where c(k) = A002430(k)/A036279(k) is the k-th positive coefficient in the Taylor series for tan(x).

1, 1, 1, 1, 1, 1, 45, 45, 315, 63, 14175, 675, 93555, 66825, 14189175, 8513505, 638512875, 70945875, 19538493975, 19538493975, 9280784638125, 40176556875, 714620417135625, 54970801318125, 147926426347074375, 11378955872851875, 48076088562799171875, 6868012651828453125

Offset

1,7

Links

Amiram Eldar, Table of n, a(n) for n = 1..450

John Greene, The Burgstahler Coincidence, The Fibonacci Quarterly, Vol. 40, No. 3 (2002), pp. 194-202.

Mathematica

c[n_] := (-1)^n * (16^n-4^n) * Zeta[1-2*n]/(2*n-1)!;
a[n_] := Denominator[Sum[Binomial[n, 2*k-2] * c[k], {k, 1, Floor[(n+1)/2]}]];
Array[a, 28]

Prog

(PARI) c(n) = (-1)^(n+1) * (16^n-4^n) * bernfrac(2*n)/(2*n)!;
a(n) = denominator(sum(k = 1, (n+1)\2, binomial(n, 2*k-2) * c(k)));

Crossrefs

Cf. A002430, A036279, A393302 (numerators).

Sequence in context: A199356 A199523 A119415 * A165866 A252721 A042011

Adjacent sequences: A393300 A393301 A393302 * A393304 A393305 A393306

Keyword

nonn,easy,frac

Author

Amiram Eldar, Feb 10 2026

Status

approved