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

0,6

Links

Table of n, a(n) for n=0..24.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Bisections are |A012115(n)| and A001818.

Sequence in context: A027608 A354657 A003297 * A080026 A060867 A192814

Adjacent sequences: A012245 A012246 A012247 * A012249 A012250 A012251

Keyword

nonn

Author

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

Extensions

More terms from Michel Marcus, Mar 09 2017

Status

approved