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

0,3

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

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 *)

Prog

(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

Crossrefs

Cf. A000594, A002408, A302200.

Sequence in context: A002019 A012878 A300452 * A263171 A003299 A198677

Adjacent sequences: A302198 A302199 A302200 * A302202 A302203 A302204

Keyword

sign

Author

N. J. A. Sloane, Apr 15 2018

Status

approved