A394319 a(n) = (2*n)! * [x^(2*n)] (C(x)'' - 2*x*C(x)' - C(x)) / 2, where C(x) satisfies C(x) = cosh( Integral C(x)^3 dx ).

0, 4, 188, 15480, 2048488, 400905884, 109134331716, 39482743670704, 18334129888716944, 10632555413767031028, 7533105574537732716940, 6403427720440475603942312, 6432629346113562245214720504, 7539415949159942835152286830860, 10197287974265084619706878434135444

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..215

Formula

a(n) = A394318(n,1).

Example

C(x)   = 1 + x^2/2! + 13*x^4/4! + 493*x^6/6! + 37369*x^8/8! + ...
C(x)'  =       x/1! + 13*x^3/3! + 493*x^5/5! + 37369*x^7/7! + ...
C(x)'' =       1    + 13*x^2/2! + 493*x^4/4! + 37369*x^6/6! + ...
(C(x)'' - 2*x*C(x)' - C(x)) / 2 = 4*x^2/2! + 188*x^4/4! + 15480*x^6/6! + 2048488*x^8/8! + ...

Crossrefs

Column k=1 of A394318.

Cf. A281181 ((2*n)! * [x^(2*n)] C(x)), A391180.

Sequence in context: A358809 A266492 A285882 * A208184 A355613 A172809

Adjacent sequences: A394316 A394317 A394318 * A394320 A394321 A394322

Keyword

nonn

Author

Seiichi Manyama, Apr 13 2026

Status

approved