A122575 Expansion of -x*(1-x)/(1+14*x+x^2)^3.

0, -1, 43, -1215, 28445, -597638, 11700450, -217941042, 3911918070, -68234265135, 1163342929477, -19468544310649, 320806889772075, -5217751119317660, 83921044722457460, -1336777733583083700, 21114347188610320476, -331025419358450069613, 5155517342468313436815, -79820563217794780940035

Offset

0,3

Comments

Based on the cubic elliptic invariant j(x)=((x^8 + 14*x^4 + 1)^3)^3/(108*x^4*(x^4 - 1)).

References

Harry Hochstadt, The Functions of Mathematical Physics, Wiley, New York (1971), p. 170; also Dover, New York (1986), 129-130.

Links

G. C. Greubel, Table of n, a(n) for n = 0..865

Mathematica

nn:=19; CoefficientList[Series[x*(x-1)/(x^2+14*x+1)^3, {x, 0, nn}], x] (* Georg Fischer, Apr 14 2020 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
[0] cat Coefficients(R!( -x*(1-x)/(1+14*x+x^2)^3 )); // G. C. Greubel, Oct 30 2024
(SageMath)
def A122575_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( -x*(1-x)/(1+14*x+x^2)^3 ).list()
A122575_list(30) # G. C. Greubel, Oct 30 2024

Crossrefs

Sequence in context: A265658 A214100 A229432 * A014938 A235646 A022220

Adjacent sequences: A122572 A122573 A122574 * A122576 A122577 A122578

Keyword

sign,easy

Author

Roger L. Bagula, Sep 17 2006

Extensions

Edited and extended by N. J. A. Sloane, Jun 27 2009

Offset changed by G. C. Greubel, Oct 30 2024

Status

approved