A013369 - OEIS

%I #16 Mar 17 2022 11:42:14

%S 1,0,0,-2,0,0,40,-2,0,-2240,480,-2,246400,-137280,8320,-44844802,

%T 51251200,-10325120,12197916160,-24831206402,11394406400,

%U -4636033573760,15296025241600,-13230894476802,2348235343872000

%N Expansion of e.g.f. exp(sin(x)-sinh(x)).

%H Seiichi Manyama, <a href="/A013369/b013369.txt">Table of n, a(n) for n = 0..592</a>

%F a(0) = 1; a(n) = -2 * Sum_{k=0..floor((n-3)/4)} binomial(n-1,4*k+2) * a(n-4*k-3). - _Seiichi Manyama_, Mar 17 2022

%e 1-2/3!*x^3+40/6!*x^6-2/7!*x^7-2240/9!*x^9...

%t With[{nn=30},CoefficientList[Series[Exp[Sin[x]-Sinh[x]],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 13 2020 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sin(x)-sinh(x)))) \\ _Seiichi Manyama_, Mar 17 2022

%o (PARI) a(n) = if(n==0, 1, -2*sum(k=0, (n-3)\4, binomial(n-1, 4*k+2)*a(n-4*k-3))); \\ _Seiichi Manyama_, Mar 17 2022

%Y Cf. A013025, A307978.

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Definition clarified by _Harvey P. Dale_, May 13 2020