A024348 Expansion of tan(x^2).

2, 240, 483840, 4704860160, 140016638361600, 9962283186074419200, 1448674564423160954880000, 386164234578290422390456320000, 174195452900540085852580211589120000, 125069935244132704803738682551120691200000, 136166701199201243586499061842886142826905600000

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..116

Formula

a(n) = A000182(n)*A001813(2*n+1). - Robert Israel, Dec 20 2018

a(n) = 2 * A009767(n). - Sean A. Irvine, Jul 01 2019

Maple

S:= series(tan(x), x, 52):
seq(coeff(S, x, 2*k+1)*(4*k+2)!, k=0..25); # Robert Israel, Dec 20 2018

Mathematica

With[{m=50}, CoefficientList[Series[Tan[x^2], {x, 0, m}], x]*Range[0, m]!][[3;; ;; 4]] (* G. C. Greubel, Jan 31 2022 *)

Prog

(Sage) [factorial(4*n+2)*( tan(x^2) ).series(x, 4*n+3).list()[4*n+2] for n in (0..20)] # G. C. Greubel, Jan 31 2022
(Magma)
m:=50; R<x>:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Tan(x^2) )));
[b[4*n-3]: n in [1..Floor((m-2)/4)]]; // G. C. Greubel, Jan 31 2022

Crossrefs

Cf. A000182, A001813.

Sequence in context: A087226 A217972 A071967 * A006523 A294319 A055968

Adjacent sequences: A024345 A024346 A024347 * A024349 A024350 A024351

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved