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

%I A302201 #15 Feb 22 2024 20:29:26
%S A302201 1,1,-7,5,193,-1273,-2707,118827,-853551,-4449558,165958491,
%T A302201 -1452523488,-8908621939,425284211536,-4941880813097,-19601696580922,
%U A302201 1717461768840017,-27768623874128015,11072293576957975,9641864176354481835
%N A302201 E.g.f.: exp (e.g.f. for the "cusp form" A002408).
%C A302201 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 A302201 Andrew Howroyd, <a href="/A302201/b302201.txt">Table of n, a(n) for n = 0..200</a>
%t A302201 eta = QPochhammer;
%t A302201 cc = CoefficientList[#, x]&;
%t A302201 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 A302201 seq[20] (* _Jean-François Alcover_, Sep 07 2019, from PARI *)
%o A302201 (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 A302201 Cf. A000594, A002408, A302200.
%K A302201 sign
%O A302201 0,3
%A A302201 _N. J. A. Sloane_, Apr 15 2018