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Expansion of e.g.f. sinh(tanh(x)*tan(x))/2 in odd powers of x^2.
1

%I #14 Jan 12 2025 12:11:17

%S 1,116,202576,1557978176,34206677698816,1706222428480541696,

%T 167325183704890858786816,29168516299952885066683006976,

%U 8389219957754997383106354075467776,3758865858584530123647466441487099887616,2506919694437630172543194103107513029881757696

%N Expansion of e.g.f. sinh(tanh(x)*tan(x))/2 in odd powers of x^2.

%H Andrew Howroyd, <a href="/A009617/b009617.txt">Table of n, a(n) for n = 0..100</a>

%e x^2/2! + 116*x^6/6! + 202576*x^10/10! + 1557978176*x^14/14! ...

%t Sinh[ Tanh[ x ]*Tan[ x ] ]/2 (* [ x^(4n+2) ] *)

%o (PARI) seq(n)={my(A=O(x^(4*n+2))); Vec(substpol(serlaplace( sinh(tanh(x + A)*tan(x + A))/2 )/x^2, x^4, x))} \\ _Andrew Howroyd_, Jan 12 2025

%Y Cf. A012671.

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested 03/97.

%E a(9) onwards from _Andrew Howroyd_, Jan 12 2025