A013209 Expansion of e.g.f. log(sech(x) + arctanh(x)).

0, 1, -2, 7, -24, 173, -1280, 11779, -120960, 1474969, -19695232, 296068991, -4847011840, 87094091589, -1687646744576, 35308668668155, -789939274514432, 18872654969343537, -478658276989173760

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

E.g.f.: log(sech(x)+arctanh(x)).

Example

x - 2/2!*x^2 + 7/3!*x^3 - 24/4!*x^4 + 173/5!*x^5 ...

Prog

(PARI) a(n)=local(y); if(n<0, 0, y=x+x*O(x^n); n!*polcoeff(log(1/cosh(y)+atanh(y)), n))

Crossrefs

Sequence in context: A330506 A236422 A013204 * A244090 A247880 A330051

Adjacent sequences: A013206 A013207 A013208 * A013210 A013211 A013212

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

a(0)=0 inserted and title improved by Sean A. Irvine, Aug 01 2018

Status

approved