A381145 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-sin(x)) ).

1, 1, 3, 15, 105, 937, 10059, 124607, 1720593, 25578001, 391041299, 5628440015, 55397475705, -847789025159, -93469767131685, -5040670692970753, -236210967512228575, -10629917015586704351, -475183316832486106589, -21394016956935371375601, -975459739630268065696887

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A002017, A381142, A381148.

Cf. A136630, A185690, A334856.

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+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} (n+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.