OFFSET
0,5
FORMULA
E.g.f.: exp(arcsinh(x)).
E.g.f. A(x) satisfies A(x) = 1/A(-x).
a(n) = Sum_{k=0..n} i^(n-k) * A385343(n,k), where i is the imaginary unit.
a(n) = A177698(n-1) for n > 1.
a(2*n+1) = 0 for n > 0.
a(n) = 2^n * n! * binomial((n+1)/2,n)/(n+1).
From Seiichi Manyama, Mar 22 2026: (Start)
E.g.f.: (1/x) * Series_Reversion( x/sqrt(1 + 2*x) ).
E.g.f. A(x) satisfies A(x) = sqrt(1 + 2*x*A(x)). (End)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(x+sqrt(x^2+1)))
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Jun 26 2025
STATUS
approved
