A013558 E.g.f. -log(sech(x) - log(x+1)).

0, 1, 1, 4, 3, 33, 155, 1195, 5418, 72373, 496027, 6851051, 59706592, 986009607, 10430165629, 193892831665, 2439695949632, 50409517110169, 737532991565959, 16755308524034767, 279581740874221016

Offset

0,4

Comments

The inner function is sech(x) - log(1+x) = 1 - x - x^3/3 + 11*x^4/24 - x^5/5 + 59*x^6/720 - x^7/7 + ... = 1 - x/1! + 0*x^2/2! - 2*x^3/3! + 11*x^4/4! - 24*x^5/5! + 59*x^6/6! - ...

Links

G. C. Greubel, Table of n, a(n) for n = 0..200

Example

x + 1/2!*x^2 + 4/3!*x^3 + 3/4!*x^4 + 33/5!*x^5 ...

Mathematica

CoefficientList[Series[-Log[Sech[x]-Log[x+1]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Nov 12 2016 *)

Crossrefs

Sequence in context: A211364 A099438 A002178 * A161000 A220363 A120078

Adjacent sequences: A013555 A013556 A013557 * A013559 A013560 A013561

Keyword

nonn

Author

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

Extensions

Offset and another leading 1 from R. J. Mathar, Dec 22 2011

a(0)=0 prepended by Vaclav Kotesovec, Nov 12 2016

Status

approved