A381174 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*cos(x)) ).

1, 1, 4, 27, 264, 3365, 52800, 980903, 20984320, 506078505, 13525493760, 394758794419, 12414039171072, 414990179398093, 14523823020621824, 521523225315049215, 18594912994237808640, 613842569215361446097, 14735570097970682265600, -228398321523777856462261

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..19.

Index entries for reversions of series

Formula

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

a(n) = Sum_{k=0..n} k! * binomial(n+k+1,k)/(n+k+1) * 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+k+1, k)/(n+k+1)*I^(n-k)*a185951(n, k));

Crossrefs

Cf. A381173, A381175, A381176.

Cf. A185951.

Sequence in context: A376107 A177379 A052813 * A218653 A359461 A121353

Adjacent sequences: A381171 A381172 A381173 * A381175 A381176 A381177

Keyword

sign

Author

Seiichi Manyama, Feb 16 2025

Status

approved