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

1, -4, 133, -15130, 4101799, -2177360656, 1999963458217, -2919514870785766, 6365117686550339275, -19765974970578036695068, 84220118333781814726917709, -477722110504065444764182065202, 3518554409906597166261453268226671, -32952557456293494405944914420304822440

Offset: 0

Author

Peter Luschny, Jul 03 2016

Keywords

• sign

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 0..166
• Eric Weisstein's MathWorld, Mittag-Leffler Function
• Wikipedia, Mittag-Leffler function

Crossrefs

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

Programs

Maple

s := series(z/((exp(z)+2*exp(-z/2)*cos(z*3^(1/2)/2))/3),z,60):
seq((n*3+1)!*coeff(s,z,n*3+1), n=0..13);

Mathematica

c = CoefficientList[Series[1/MittagLefflerE[3,z^3],{z,0,15*3}],z];
Table[Factorial[3*n+1]*c[[3*n+1]], {n,0,13}]

Formula

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

For n >= 1, a(n) = -Sum_{k=0..n-1} a(k) binomial(3n+1,3k+1). - Robert Israel, Jul 03 2016