A381310 E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^(1/2)) / A(x)^(1/2) ).

1, 1, 1, 0, -7, -38, -111, 259, 7025, 59752, 209297, -2545257, -59541487, -609139048, -1257456543, 86370090271, 1968628674465, 20998208227456, -60103780767519, -7806917233342465, -175430347192682527, -1683391495632464904, 26661441929560502097, 1550891419460475900175

Offset: 0

Author

Seiichi Manyama, Feb 19 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, (n/2-k/2+1)^(k-1)*I^(n-k)*a136630(n, k));

Formula

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