A381413 E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) / A(x)^2 ).

1, 1, 1, 0, -19, -248, -2355, -14504, 69113, 4886848, 117560921, 1925294976, 14523966437, -478472693632, -28832809713435, -921278399444480, -18983574162924687, -55161522627854336, 18306724696454977713, 1118400460045234098176, 41755736397548337559133

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• sign

Crossrefs

Cf. A136630.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (2*n-2*k+1)^(k-1)*I^(n-k)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} (2*n-2*k+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.