A013195 E.g.f.: log(sec(x) + arcsin(x)).

0, 1, 0, 0, 4, -12, 72, -168, 544, 8144, -91520, 1384768, -11984128, 149032128, -1158162432, 16299168896, -125837340672, 2859883876608, -32260942757888, 1008997773326336, -15535095938220032, 466978134769624064

Offset

0,5

Links

Matthew House, Table of n, a(n) for n = 0..449

Example

G.f. = x + 4*x^4 - 12*x^5 + 72*x^6 - 168*x^7 + 544*x^8 + 8144*x^9 - 91520*x^10 + ...

Mathematica

With[{nn=30}, CoefficientList[Series[Log[Sec[x]+ArcSin[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 05 2021 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); n! * polcoeff( log( 1 / cos(x + A) + asin(x + A) ), n))}; /* Michael Somos, Feb 17 2017 */

Crossrefs

Sequence in context: A121771 A009621 A335907 * A356667 A323295 A166746

Adjacent sequences: A013192 A013193 A013194 * A013196 A013197 A013198

Keyword

sign

Author

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

Extensions

a(0) corrected by Matthew House, Feb 16 2017

New name from Michael Somos, Feb 16 2017

Status

approved