A274704 Exponential generating function 1/M_{4}(z^4) where M_{n}(z) is the n-th Mittag-Leffler function, nonzero coefficients only.

1, -5, 621, -437593, 1026405753, -6054175060941, 75477454065058725, -1766732850877953050849, 71248914440011028226682737, -4637564239713542128355021380117, 462852368857623061805761137170608989, -67965094887205237792816627191801312013545

Offset: 0

Author

Peter Luschny, Jul 03 2016

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..128

Crossrefs

Cf. A181983 (n=1), A009843 (n=2), A274703 (n=3), A274705 (array).

Programs

Maple

s := series(2*z/(cosh(z)+cos(z)),z,60):
seq((4*n+1)!*coeff(s,z,4*n+1),n=0..11);

Mathematica

c = CoefficientList[Series[1/MittagLefflerE[4, z^4], {z, 0, 15*4}], z];
Table[Factorial[4*n+1]*c[[4*n+1]], {n, 0, 12}]

Formula

E.g.f. (nonzero coefficients): 2*z/(cosh(z)+cos(z)).

For n >= 1, a(n) = - Sum_{k=0..n-1} a(k)*binomial(4*k+1,4*n+1). - Robert Israel, Jul 04 2016