A009497 - OEIS

%I #21 Jan 12 2025 12:11:08

%S 1,-64,25216,-31711744,93380755456,-538721831747584,

%T 5434440423098023936,-88353705160970793385984,

%U 2179843711161864280506105856,-77903078128153520290915516678144,3885493817309637834095425199974383616,-262391914253566550682675647373292878168064

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

%H Andrew Howroyd, <a href="/A009497/b009497.txt">Table of n, a(n) for n = 0..100</a>

%e x^2/2! - 64*x^6/6! + 25216*x^10/10! - 31711744*x^14/14! ...

%t With[{nn=50},Take[CoefficientList[Series[Sin[Sinh[x]*Sin[x]]/2,{x,0,nn}],x] Range[0,nn]!,{3,-1,4}]] (* _Harvey P. Dale_, Oct 08 2017 *)

%o (PARI) seq(n)={my(A=O(x^(4*n+2))); Vec(substpol(serlaplace( sin(sinh(x+A)*sin(x+A))/2 )/x^2, x^4, x))} \\ _Andrew Howroyd_, Jan 11 2025

%Y Cf. A012524.

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended by _Olivier Gérard_, Mar 15 1997

%E Prior Mathematica program replaced by _Harvey P. Dale_, Oct 08 2017

%E a(10) onwards from _Andrew Howroyd_, Jan 11 2025