A381144 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * cos(x)) ).

1, 1, 3, 13, 65, 221, -2933, -120903, -3104127, -71637191, -1562635789, -31373685947, -505087300991, -1692007785259, 402032879446395, 28152810613025521, 1423083552938781697, 62552808878706976625, 2459148829654813484131, 82692880516086149155581

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• sign

Comments

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

Links

• Index entries for reversions of series

Crossrefs

Cf. A009189, A381141, A381146.

Cf. A185951.

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

Formula

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

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