A274703 - OEIS

%I #19 Jul 04 2016 06:22:39

%S 1,-4,133,-15130,4101799,-2177360656,1999963458217,-2919514870785766,

%T 6365117686550339275,-19765974970578036695068,

%U 84220118333781814726917709,-477722110504065444764182065202,3518554409906597166261453268226671,-32952557456293494405944914420304822440

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

%C For references see also A274705 which is the main entry for this sequence of sequences.

%H Robert Israel, <a href="/A274703/b274703.txt">Table of n, a(n) for n = 0..166</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Mittag-LefflerFunction.html">Mittag-Leffler Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Mittag-Leffler_function">Mittag-Leffler function</a>

%F E.g.f. (nonzero coefficients): z/((exp(z)+2*exp(-z/2)*cos(z*3^(1/2)/2))/3).

%F For n >= 1, a(n) = -Sum_{k=0..n-1} a(k) binomial(3n+1,3k+1). - _Robert Israel_, Jul 03 2016

%p s := series(z/((exp(z)+2*exp(-z/2)*cos(z*3^(1/2)/2))/3),z,60):

%p seq((n*3+1)!*coeff(s,z,n*3+1), n=0..13);

%t c = CoefficientList[Series[1/MittagLefflerE[3,z^3],{z,0,15*3}],z];

%t Table[Factorial[3*n+1]*c[[3*n+1]], {n,0,13}]

%Y Cf. A181983 (n=1), A009843 (n=2), A274704 (n=4), A274705 (array).

%K sign

%O 0,2

%A _Peter Luschny_, Jul 03 2016