A354138 a(n) is the numerator of Sum_{k=0..n} (-1)^k / (2*k)!.

1, 1, 13, 389, 4357, 1960649, 258805669, 47102631757, 11304631621681, 691843455246877, 1314502564969066301, 607300185015708631061, 335229702128671164345673, 217899306383636256824687449, 32946375125205802031892742289, 848027998784883070051677094421

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

Numerators of coefficients in expansion of cos(sqrt(x)) / (1 - x).

Example

1, 1/2, 13/24, 389/720, 4357/8064, 1960649/3628800, 258805669/479001600, ...

Mathematica

Table[Sum[(-1)^k/(2 k)!, {k, 0, n}], {n, 0, 15}] // Numerator
nmax = 15; CoefficientList[Series[Cos[Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator

Prog

(PARI) a(n) = numerator(sum(k=0, n, (-1)^k/(2*k)!)); \\ Michel Marcus, May 24 2022

Crossrefs

Cf. A010050, A049470, A053557, A061354, A103816, A120265, A143382, A354211, A354332, A354334, A354378 (denominators).

Sequence in context: A370379 A302700 A194489 * A356740 A275651 A203972

Adjacent sequences: A354135 A354136 A354137 * A354139 A354140 A354141

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 24 2022

Status

approved