A302610 Expansion of e.g.f. -log(1 - x)*arcsinh(x).

0, 0, 2, 3, 4, 20, 158, 819, 3624, 33984, 427482, 3819915, 29665260, 404822340, 6948032310, 88407058635, 991515848400, 17715286764000, 383952670412850, 6349179054589875, 93532380775766100, 2063197602667372500, 53913667654307868750, 1098018631195048591875

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Examples

			-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! + ...
		

Crossrefs

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

Programs

Maple

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

Mathematica

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

Formula

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