A024343 Expansion of e.g.f. sin(x^2) in powers of x^(4*n + 2).

2, -120, 30240, -17297280, 17643225600, -28158588057600, 64764752532480000, -202843204931727360000, 830034394580628357120000, -4299578163927654889881600000, 27500101936481280675682713600000

Offset

0,1

Comments

Absolute values are coefficients of expansion of sinh(x^2).

Links

G. C. Greubel, Table of n, a(n) for n = 0..175

Formula

a(n) = (-1)^n * (4*n+2)! / (2*n+1)!.

E.g.f.: [x^(4*n+2)] sin(x^2)

a(n) = 2 * A009564(n). - Sean A. Irvine, Jul 01 2019

Mathematica

Table[(-1)^n*(2*n+1)!*Binomial[4*n+2, 2*n+1], {n, 0, 30}] (* G. C. Greubel, Jan 29 2022 *)

Prog

(PARI) a(n)=polcoeff(serlaplace(sin(x^2)), 4*n+2)
(PARI) a(n)=(-1)^n*(4*n+2)!/(2*n+1)!
(Sage) f=factorial; [(-1)^n*f(4*n+2)/f(2*n+1) for n in (0..30)] # G. C. Greubel, Jan 29 2022
(Magma) F:=Factorial;; [(-1)^n*F(4*n+2)/F(2*n+1) : n in [0..30]]; // G. C. Greubel, Jan 29 2022

Crossrefs

Bisection of A001813.

Cf. A009564.

Sequence in context: A272180 A187880 A331500 * A100043 A181760 A290247

Adjacent sequences: A024340 A024341 A024342 * A024344 A024345 A024346

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Edited by Ralf Stephan, Mar 25 2004

Name edited by Michel Marcus, Jul 01 2019

Status

approved