A381142 Expansion of e.g.f. exp( -LambertW(-sin(x)) ).

1, 1, 3, 15, 113, 1137, 14355, 218239, 3883585, 79218721, 1822842243, 46717337007, 1319891043569, 40759239427857, 1365932381706963, 49373610759452575, 1914856819983977473, 79316216447375396161, 3494800326874932467331, 163218136611270923087439

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A002017, A381145, A381148.

Cf. A136630, A185690, A277498.

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

Formula

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

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