A179984 Numerators of Integral_{x=0..1} cos(log(x))^n dx.

1, 1, 3, 2, 41, 9, 263, 101, 15357, 7597, 284603, 43116, 38393473, 529897, 546720327, 5670211, 26605516873, 92136441, 484386120331, 7980112918, 37169988225261, 677746663297, 17315548435192687, 86554551096513, 9627544465660584149, 2094684707932493

Offset

0,3

Links

Amiram Eldar, Table of n, a(n) for n = 0..669

Formula

a(n) = numerator(2^(-n)*Sum_{k=0..n} C(n,k)/(1+(n-2k)^2)). - Amit Lanis, Nov 18 2022

Mathematica

Table[Numerator[Integrate[Cos[Log[x]]^k, {x, 0, 1}]], {k, 0, 20}]

Crossrefs

Cf. A180092 (denominators).

Sequence in context: A370825 A009084 A096057 * A260888 A065085 A321169

Adjacent sequences: A179981 A179982 A179983 * A179985 A179986 A179987

Keyword

nonn,frac

Author

Vladimir Reshetnikov, Jan 17 2011

Extensions

More terms from Amiram Eldar, Jul 07 2021

Status

approved