A381261 Expansion of e.g.f. exp( -LambertW(-2 * x * cos(x)) / 2 ).

1, 1, 5, 46, 669, 13176, 328153, 9889328, 349998169, 14232282112, 653960139021, 33511444515968, 1894938691013173, 117209395966704640, 7872535432641217185, 570622024676568564736, 44395462114163659522353, 3690312836780077587120128, 326399124496126009678138261

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• nonn

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A185951, A381141.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (2*k+1)^(k-1)*I^(n-k)*a185951(n, k));

Formula

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

a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.