login
Expansion of e.g.f. -log(1 - x)*arcsinh(x).
1

%I #7 Mar 27 2019 03:51:51

%S 0,0,2,3,4,20,158,819,3624,33984,427482,3819915,29665260,404822340,

%T 6948032310,88407058635,991515848400,17715286764000,383952670412850,

%U 6349179054589875,93532380775766100,2063197602667372500,53913667654307868750,1098018631195048591875

%N Expansion of e.g.f. -log(1 - x)*arcsinh(x).

%F E.g.f.: -log(1 - x)*log(x + sqrt(1 + x^2)).

%e -log(1 - x)*arcsinh(x) = 2*x^2/2! + 3*x^3/3! + 4*x^4/4! + 20*x^5/5! + 158*x^6/6! + 819*x^7/7! + 3624*x^8/8! + ...

%p a:=series(-log(1-x)*arcsinh(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 26 2019

%t nmax = 23; CoefficientList[Series[-Log[1 - x] ArcSinh[x], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A009410, A009416, A009429, A009435, A012572, A104150, A177699, A177700, A296435, A296727, A302611.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 10 2018