OFFSET
0,3
FORMULA
E.g.f.: (1/x) * Series_Reversion( x * exp(-arcsinh(4*x)/4) ).
E.g.f.: ( (1/x) * Series_Reversion( x/(1 + 8*x)^(5/8) ) )^(1/5).
E.g.f. A(x) satisfies A(x) = exp( (1/4) * arcsinh(4*x*A(x)) ).
E.g.f. A(x) satisfies A(x) = (1 + 8*x*A(x)^5)^(1/8).
a(n) = 8^n * n! * binomial((5*n+1)/8,n)/(5*n+1).
a(n) = Sum_{k=0..n} (n+1)^(k-1) * (4*i)^(n-k) * A385343(n,k), where i is the imaginary unit.
a(8*n+3) = 0 for n >= 0.
PROG
(PARI) a(n) = 8^n*n!*binomial((5*n+1)/8, n)/(5*n+1);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 29 2025
STATUS
approved
