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Search: id:A074059
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| A074059 |
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Dimension of the cohomology ring of the moduli space of n-pointed curves of genus 0 satisfying the associativity equations of physics (also known as the WDVV equations). |
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+0
4
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| 1, 1, 2, 7, 34, 213, 1630, 14747, 153946, 1821473, 24087590, 352080111, 5636451794, 98081813581, 1843315388078, 37209072076483, 802906142007946, 18443166021077145, 449326835001457846
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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B. Drake, I. M. Gessel and G. Xin, Three proofs and a generalization of the Goulden-Litsyn-Shevelev conjecture ..., J. Integer Sequences, Vol. 10 (2007), #07.3.7.
I. P. Goulden, S. Litsyn and V. Shevelev, On a Sequence Arising in Algebraic Geometry, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.7.
S. Keel, Intersection theory of moduli space of stable n-pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992), 545-574.
M. Kontsevich and Y. Manin, Quantum cohomology of a product (with Appendix by R. Kaufmann), Inv. Math. 124, f. 1-3 (1996) 313-339.
Margaret Readdy, The pre-WDVV ring of physics and its topology. The Ramanujan Journal, Special issue on the Number Theory and Combinatorics in Physics, 10 (2005), 269-281.
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FORMULA
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The exponential generating function A = A(x) = sum_{n>=1} a(n) x^n/n! satisfies the equation (1+A)log(1+A) = 2A-x. Explicitly, 1+A(x) = exp(2+W(e^(-2)(2+x))), where W is Lambert's W-function. - Ira Gessel (gessel(AT)brandeis.edu), Dec 15 2005
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MAPLE
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series(exp(LambertW(-exp(-2)*(2+x))+2)-1, x, 30): A:=simplify(%, symbolic): A074059:=n->n!*coeff(A, x, n): (Gessel)
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CROSSREFS
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Cf. A074060.
Sequence in context: A112916 A002720 A111539 this_sequence A135882 A049463 A029894
Adjacent sequences: A074056 A074057 A074058 this_sequence A074060 A074061 A074062
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KEYWORD
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nonn
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AUTHOR
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Margaret A. Readdy (readdy(AT)ms.uky.edu), Aug 16 2002
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EXTENSIONS
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More terms from Ira Gessel (gessel(AT)brandeis.edu), Dec 15 2005
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