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A274703 Exponential generating function 1/M_{3}(z^3) where M_{n}(z) is the n-th Mittag-Leffler function, nonzero coefficients only.

%I A274703 #20 Feb 16 2025 08:33:36
%S A274703 1,-4,133,-15130,4101799,-2177360656,1999963458217,-2919514870785766,
%T A274703 6365117686550339275,-19765974970578036695068,
%U A274703 84220118333781814726917709,-477722110504065444764182065202,3518554409906597166261453268226671,-32952557456293494405944914420304822440
%N A274703 Exponential generating function 1/M_{3}(z^3) where M_{n}(z) is the n-th Mittag-Leffler function, nonzero coefficients only.
%C A274703 For references see also A274705 which is the main entry for this sequence of sequences.
%H A274703 Robert Israel, <a href="/A274703/b274703.txt">Table of n, a(n) for n = 0..166</a>
%H A274703 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Mittag-LefflerFunction.html">Mittag-Leffler Function</a>
%H A274703 Wikipedia, <a href="http://en.wikipedia.org/wiki/Mittag-Leffler_function">Mittag-Leffler function</a>
%F A274703 E.g.f. (nonzero coefficients): z/((exp(z)+2*exp(-z/2)*cos(z*3^(1/2)/2))/3).
%F A274703 For n >= 1, a(n) = -Sum_{k=0..n-1} a(k) binomial(3n+1,3k+1). - _Robert Israel_, Jul 03 2016
%p A274703 s := series(z/((exp(z)+2*exp(-z/2)*cos(z*3^(1/2)/2))/3),z,60):
%p A274703 seq((n*3+1)!*coeff(s,z,n*3+1), n=0..13);
%t A274703 c = CoefficientList[Series[1/MittagLefflerE[3,z^3],{z,0,15*3}],z];
%t A274703 Table[Factorial[3*n+1]*c[[3*n+1]], {n,0,13}]
%Y A274703 Cf. A181983 (n=1), A009843 (n=2), A274704 (n=4), A274705 (array).
%K A274703 sign
%O A274703 0,2
%A A274703 _Peter Luschny_, Jul 03 2016