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%I A013025 #17 Mar 17 2022 11:42:11
%S A013025 1,2,4,8,16,34,88,296,1152,4546,17696,72712,343424,1843170,10274688,
%T A013025 56506024,315332608,1910439298,12815815168,90064672520,629185325056,
%U A013025 4400756254114,32422278027264,258933905154856,2168521319694336
%N A013025 Expansion of e.g.f. exp(sinh(x) + sin(x)).
%H A013025 Harvey P. Dale, <a href="/A013025/b013025.txt">Table of n, a(n) for n = 0..500</a>
%F A013025 a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(n-4*k-1). - _Seiichi Manyama_, Mar 17 2022
%e A013025 1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+34/5!*x^5...
%t A013025 With[{nn=30},CoefficientList[Series[Exp[Sinh[x]+Sin[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 17 2011 *)
%o A013025 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sin(x)+sinh(x)))) \\ _Seiichi Manyama_, Mar 17 2022
%o A013025 (PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\4, binomial(n-1, 4*k)*a(n-4*k-1))); \\ _Seiichi Manyama_, Mar 17 2022
%Y A013025 Cf. A013369, A306347.
%K A013025 nonn
%O A013025 0,2
%A A013025 Patrick Demichel (patrick.demichel(AT)hp.com)

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