A302201 E.g.f.: exp (e.g.f. for the "cusp form" A002408).

1, 1, -7, 5, 193, -1273, -2707, 118827, -853551, -4449558, 165958491, -1452523488, -8908621939, 425284211536, -4941880813097, -19601696580922, 1717461768840017, -27768623874128015, 11072293576957975, 9641864176354481835

Offset: 0

Author

N. J. A. Sloane, Apr 15 2018

Keywords

• sign

Comments

Whenever there is an important cusp form (such as A002408, or the Ramanujan tau or Delta function A000594), with e.g.f. C(x), say, it seems that the sequence with e.g.f. exp(C(x)) should also have some interesting properties.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000594, A002408, A302200.

Programs

Mathematica

eta = QPochhammer;
cc = CoefficientList[#, x]&;
seq[n_] := Module[{A}, A = O[x]^n; cc[Exp[(cc[x*(eta[x + A]*(eta[x^4 + A]/eta[x^2 + A]))^8]*cc[Exp[x + x*A]]) . x^Range[0, n]] + O[x]^n]* Range[0, n-1]!];
seq[20] (* Jean-François Alcover, Sep 07 2019, from PARI *)

PARI

seq(n)={my(A=O(x^n)); Vec(serlaplace(exp(serconvol(x*(eta(x + A) * eta(x^4 + A) / eta(x^2 + A))^8, exp(x + x*A)))))} \\ Andrew Howroyd, Nov 04 2018