A302201 - OEIS

%I #15 Feb 22 2024 20:29:26

%S 1,1,-7,5,193,-1273,-2707,118827,-853551,-4449558,165958491,

%T -1452523488,-8908621939,425284211536,-4941880813097,-19601696580922,

%U 1717461768840017,-27768623874128015,11072293576957975,9641864176354481835

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

%C 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.

%H Andrew Howroyd, <a href="/A302201/b302201.txt">Table of n, a(n) for n = 0..200</a>

%t eta = QPochhammer;

%t cc = CoefficientList[#, x]&;

%t 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]!];

%t seq[20] (* _Jean-François Alcover_, Sep 07 2019, from PARI *)

%o (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

%Y Cf. A000594, A002408, A302200.

%K sign

%O 0,3

%A _N. J. A. Sloane_, Apr 15 2018