A012386 Expansion of e.g.f. sech(tan(x)*arcsin(x)) (only even powers).

1, 0, -12, -360, -7280, 504000, 121581504, 14369939584, 56810973440, -657138821830656, -255226784793623552, -45397358372525164544, 15722139759017802895360, 20152649683846086682296320, 10036078628535555546087604224, 107025768929375403705553551360, -5551063965616243360599603726450688

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

E.g.f. = 1 - 12/4!*x^4 - 360/6!*x^6 - 7280/8!*x^8 + ...

Mathematica

With[{nn=32}, Take[CoefficientList[Series[Sech[Tan[x]ArcSin[x]], {x, 0, nn}], x]*Range[0, nn]!, {1, -1, 2}]] (* Stefano Spezia, Dec 27 2025 *)

Crossrefs

Sequence in context: A012553 A128043 A012431 * A130213 A012633 A395124

Adjacent sequences: A012383 A012384 A012385 * A012387 A012388 A012389

Keyword

sign

Author

Patrick Demichel

Extensions

a(14)-a(16) from Stefano Spezia, Dec 27 2025

Status

approved