A381173 Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cos(x)) ).

1, 1, 2, 3, -24, -475, -5760, -52297, -155008, 8781705, 313344000, 6966991339, 102864807936, 18664712365, -71473582229504, -3387816787568865, -103478592573112320, -1899945146589964783, 18941335827815596032, 3808766537454425974739, 215681241589289359769600

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)) ).

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

Prog

(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, k!*binomial(n+1, k)*I^(n-k)*a185951(n, k))/(n+1);

Crossrefs

Cf. A381174, A381175, A381176.

Cf. A162653, A381171, A381181.

Cf. A185951.

Sequence in context: A013318 A374858 A372737 * A193338 A326226 A291262

Adjacent sequences: A381170 A381171 A381172 * A381174 A381175 A381176

Keyword

sign

Author

Seiichi Manyama, Feb 16 2025

Status

approved