A009566 Expansion of e.g.f. sinh(log(1+log(1+x))).

0, 1, -2, 8, -47, 359, -3349, 36756, -462972, 6574704, -103861896, 1805930928, -34267701720, 704555489832, -15601914340440, 370195510608192, -9369769657984128, 251979258929744448, -7175127496412091456

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..415

Programs

Mathematica

CoefficientList[Series[(Log[1 + x]*(2 + Log[1 + x]))/(2*(1 + Log[1 + x]) ), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Log[1 + x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 21 2018 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(serlaplace(sinh(log(1+log(1+x)))))) \\ G. C. Greubel, Jan 21 2018

Formula

a(n) ~ n! * (-1)^(n+1) * exp(n) / (2 * (exp(1)-1)^(n+1)). - Vaclav Kotesovec, Jan 23 2015

a(n) = (-1)^(n-1)*((n-1)! + A007840(n))/2 for n > 0. - Velin Yanev, May 17 2024

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997