A385428 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)) / A(x) ).

1, 1, 1, 0, -11, -80, -219, 3416, 68265, 550656, -3285975, -194101248, -3177823395, -5431320960, 1202586098637, 35658624599040, 359507959906641, -12186663090266112, -677861502762897711, -13768767870225444864, 126162451289700276165, 19553934035547470168064

Offset: 0

Author

Seiichi Manyama, Jun 28 2025

Keywords

• sign

Crossrefs

Cf. A001147, A385425.

Cf. A381147, A385343, A385369.

Programs

PARI

a385343(n, k) = my(x='x+O('x^(n+1))); n!*polcoef(asin(x)^k/k!, n);
a(n) = sum(k=0, n, (n-k+1)^(k-1)*I^(n-k)*a385343(n, k));

Formula

E.g.f. A(x) satisfies A(x) = ( x*A(x) + sqrt((x*A(x))^2 + 1) )^(1/A(x)).

a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.