A381263 Expansion of e.g.f. exp( -LambertW(-2 * sin(x)) / 2 ).

1, 1, 5, 48, 709, 14152, 356793, 10882648, 389790889, 16040853568, 745908722477, 38681745244032, 2213527304014189, 138556837227204736, 9417928265797994145, 690818806495197538816, 54391227913053881634001, 4575388875753714015748096, 409532433006878699321370197

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381142.

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*k+1)^(k-1)*I^(n-k)*a136630(n, k));

Formula

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

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