A328554 Coefficients in Göttsche's universal power series B_1(q) arising from enumeration of d-nodal curves in a linear system of dimension d on an algebraic surface.

1, -1, -5, 39, -345, 2961, -24866, 207759, -1737670, 14584625, -122937305, 1040906771, -8852158628, 75598131215, -648168748072, 5577807139921, -48163964723088, 417210529188188, -3624610235789053, 31575290280786530, -275758194822813754

Offset

0,3

Comments

The power series appears to be well defined, only the interpretation is conjectural.

Now proved by Tzeng. - Andrey Zabolotskiy, Jun 22 2021

Links

Table of n, a(n) for n=0..20.

Lothar Göttsche, A conjectural generating function for numbers of curves on surfaces, Communications in mathematical physics 196.3 (1998): 523-533. Also arXiv:alg-geom/9711012, Nov 1997.

Yu-jong Tzeng, A proof of the Göttsche-Yau-Zaslow formula, Stanford University, 2010.

Formula

B_1(q) = 1 - q - 5*q^2 + 39*q^3 - 345*q^4 + 2961*q^5 - 24866*q^6 + 207759*q^7 - 1737670*q^8 + 14584625*q^9 - 122937305*q^10 + 1040906771*q^11 - 8852158628*q^12 + 75598131215*q^13 - 648168748072*q^14 + 5577807139921*q^15 - 48163964723088*q^16 + 417210529188188*q^17 - 3624610235789053*q^18 + 31575290280786530*q^19 - 275758194822813754*q^20 + ...

Crossrefs

Cf. A328555.

Sequence in context: A356622 A273019 A244039 * A213233 A115187 A378919

Adjacent sequences: A328551 A328552 A328553 * A328555 A328556 A328557

Keyword

sign

Author

N. J. A. Sloane, Oct 29 2019

Extensions

Missing a(1) = -1 inserted by Andrey Zabolotskiy, Jun 22 2021

Status

approved