A012248 Expansion of e.g.f. exp(arcsinh(arcsin(x))).

1, 1, 1, 1, 1, 9, 49, 225, 897, 11025, 96801, 893025, 6803457, 108056025, 1275363153, 18261468225, 207592347393, 4108830350625, 60889593787713, 1187451971330625, 17888210916886017, 428670161650355625, 7679611833095218545, 189043541287806830625, 3530100224793651058305

Offset: 0

Author

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

Keywords

• nonn

Examples

			1 + x + 1/2!*x^2 + 1/3!*x^3 + 1/4!*x^4 + 9/5!*x^5...
		

Crossrefs

Bisections are |A012115(n)| and A001818.

Programs

Mathematica

With[{nn=25},CoefficientList[Series[Exp[ArcSinh[ArcSin[x]]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Nov 02 2020 *)

PARI

x = 'x + O('x^30); Vec(serlaplace(exp(asinh(asin(x))))) \\ Michel Marcus, Mar 09 2017

Formula

E.g.f.: Q(0)-1, where Q(k) = 2 + arcsin(x)/(1 - arcsin(x)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 19 2013

Extensions

More terms from Michel Marcus, Mar 09 2017