The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A012109 sec(arcsin(sinh(x)))=1+1/2!*x^2+13/4!*x^4+421/6!*x^6+26713/8!*x^8... 1
 1, 1, 13, 421, 26713, 2794441, 436186213, 95033434861, 27555582190513, 10260037095841681, 4771143086720391613, 2710025439753915534901, 1846296024220715321941513, 1486014763274444231870834521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..13. FORMULA From Michael Somos, May 05 2017: (Start) E.g.f.: Sum_{n>=0} a(n) * x^(2*n) / (2*n)! = sec(arcsin(sinh(x))) = 1 / sqrt(1 - sinh(x)^2). E.g.f.: Sum_{n>=0} a(n) * x^(2*n+1) / (2*n+1)! = F(i x| -1) / i where F(phi|m) is the elliptic integral of the 1st kind. E.g.f. 1 / sqrt(1 - sinh(x)^2) = y satisfies 0 = y''*y + 2*y^2 - 3*y^4 - 3*y'^2 = y - 6*y^3 + 6*y^5 - y''. a(n) = A012261(2*n). (End) EXAMPLE G.f. = 1 + x + 13*x^2 + 421*x^3 + 26713*x^4 + 2794441*x^5 + ... MATHEMATICA a[ n_] := If[ n < 0, 0, With[ {m = 2 n + 1}, m! SeriesCoefficient[ EllipticF[ I x, -1] / I, {x, 0, m}]]]; (* Michael Somos, May 05 2017 *) a[ n_] := If[ n < 0, 0, With[ {m = 2 n}, m! SeriesCoefficient[ 1 / Sqrt[1 - Sinh[x]^2], {x, 0, m}]]]; (* Michael Somos, May 05 2017 *) PROG (PARI) {a(n) = my(m); if( n<0, 0, m = 2*n; m! * polcoeff( 1 / sqrt(1 - sinh(x + x * O(x^m))^2), m))}; /* Michael Somos, May 05 2017 */ CROSSREFS Cf. A012261. Sequence in context: A081442 A100872 A012045 * A012084 A114759 A260871 Adjacent sequences: A012106 A012107 A012108 * A012110 A012111 A012112 KEYWORD nonn AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 2 08:40 EDT 2023. Contains 363090 sequences. (Running on oeis4.)