A381414 E.g.f. A(x) satisfies A(x) = exp( 2 * sin(x * A(x)) / A(x) ).

1, 2, 4, 6, -32, -686, -8256, -72394, -200448, 11160866, 373370880, 7696016614, 100295200768, -338643776142, -77999443329024, -3211092423560938, -85537972638318592, -1169784729390416830, 33029632126142382080, 3381750252027454249926, 158090250687453045194752

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• sign

Crossrefs

Cf. A136630, A381413.

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) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*I^(n-k)*a136630(n, k));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381413.

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