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Expansion of e.g.f. sinh(tan(x))*sin(x) (even powers only).
2

%I #36 Aug 04 2024 03:05:02

%S 0,2,8,168,5760,310304,23894144,2481859968,333725331456,

%T 56329065984512,11650274400684032,2895770490247219200,

%U 851263005980215443456,292012329049579197046784,115560631410392130840461312,52240866338892496235877335040

%N Expansion of e.g.f. sinh(tan(x))*sin(x) (even powers only).

%H G. C. Greubel, <a href="/A009606/b009606.txt">Table of n, a(n) for n = 0..239</a>

%F a(n) = 2*A024259(n).

%p seq(factorial(k) * coeftayl(sinh(tan(x))*sin(x), x = 0, k), k=0..30, 2); # _Muniru A Asiru_, Feb 01 2018

%t With[{nn=40},Take[CoefficientList[Series[Sinh[Tan[x]]Sin[x],{x,0,nn}], x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Dec 27 2011 *)

%o (PARI) my(x='x+O('x^40)); v=Vec(serlaplace(sinh(tan(x))*sin(x))); concat([0], vector(#v\2,n,v[2*n-1])) \\ _G. C. Greubel_, Jan 30 2018

%Y Cf. A024259.

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested by _Olivier GĂ©rard_, Mar 15 1997

%E More terms from _Harvey P. Dale_, Dec 27 2011