A013525 E.g.f.: x + (gdinv x - sinh x)/2, where gdinv = inverse-Gudermannian. Sequence has odd-indexed coefficients; others are zero.

1, 0, 2, 30, 692, 25260, 1351382, 99680490, 9695756072, 1202439837720, 185185594118762, 34674437196568950, 7757267081778543452, 2043536254646561946180, 626129820701814932734142, 220771946624511552276841410

Offset

0,3

Comments

Also gdinv(x) = log(tan(x) + sec(x)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..200

Formula

For n>0, a(n) = (1/2) * (A000364(n) - 1).

Example

x + (gdinv x - sinh x)/2 = x + 2/5!*x^5 + 30/7!*x^7 + 692/9!*x^9 + ...

Mathematica

With[{nn=40}, Take[CoefficientList[Series[x+(InverseGudermannian[x]-Sinh[ x])/2, {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Oct 16 2014 *)

Crossrefs

Sequence in context: A363113 A160694 A278884 * A270531 A229781 A114938

Adjacent sequences: A013522 A013523 A013524 * A013526 A013527 A013528

Keyword

nonn,easy

Author

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

Extensions

Definition corrected by Ralf Stephan and Don Reble, Dec 16 2004

Status

approved