Search: id:A074060
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%I A074060
%S A074060 1,1,1,1,5,1,1,16,16,1,1,42,127,42,1,1,99,715,715,99,1,1,219,3292,
%T A074060 7723,3292,219,1,1,466,13333,63173,63173,13333,466,1,1,968,49556,
%U A074060 429594,861235,429594,49556,968,1,1,1981,173570,2567940,9300303,9300303,
               2567940,173570,1981,1
%N A074060 Graded 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).
%C A074060 Combinatorial interpretations of Lagrange inversion (A134685) and the 
               2-restricted Stirling numbers of the first kind (A049444 and A143491) 
               provide a combinatorial construction for A074060 (see first Copeland 
               link). For relations of A074060 to other arrays see second Copeland 
               link page 19. [From Tom Copeland (tcjpn(AT)msn.com), Sep 28 2008]
%D A074060 S. Keel, Intersection theory of moduli space of stable n-pointed curves 
               of genus zero, Trans. Amer. Math. Soc. 330 (1992), 545-574.
%D A074060 M. Kontsevich and Y. Manin, Quantum cohomology of a product (with Appendix 
               by R. Kaufmann), Inv. Math. 124, f. 1-3 (1996) 313-339.
%D A074060 M. A. Readdy, The pre-WDVV ring of physics and its topology, preprint, 
               2002.
%H A074060 Tom Copeland, <a href="http://tcjpn.spaces.live.com/default.aspx">Combinatorics 
               of OEIS-A074060</a> Posted Sept. 2008 [From Tom Copeland (tcjpn(AT)msn.com), 
               Sep 28 2008]
%H A074060 Tom Copeland, <a href="http://tcjpn.spaces.live.com/default.aspx">Mathemagical 
               Forests v2</a> Posted June 2008 [From Tom Copeland (tcjpn(AT)msn.com), 
               Sep 28 2008]
%F A074060 Define offset to be 0 and P(n,t) = (-1)^n sum(j=0,...,n-2) a(n-2,j) * 
               t^j with P(1,t) = -1 and P(0,t) = 1, then H(x,t) = -1 + exp[P(.,t)*x] 
               is the compositional inverse in x about 0 of G(x,t) in A049444. H(x,
               0) = exp(-x) - 1, H(x,1) = -1 + exp{ 2 + W[ -exp(-2) * (2-x) ] } 
               and H(x,2) = 1 - (1+2x)^(1/2), where W is a branch of the Lambert 
               function such that W[ -2*e^(-2)] = -2 . - Tom Copeland (tcjpn(AT)msn.com), 
               Feb 17 2008
%F A074060 Let offset=0 and g(x,t) = (1-t)/[(1+x)^(t-1)-t], then the n-th row polynomial 
               of the table is given by [(g(x,t)D_x)^(n+1)]x with the derivative 
               evaluated at x=0. - Tom Copeland (tcjpn(AT)msn.com), Jun 01 2008
%e A074060 Viewed as a triangular array, the values are: 1; 1 1; 1 5 1; 1 16 16 
               1; 1 42 127 42 1; ...
%p A074060 DA:=((1+t)*A(u,t)+u)/(1-t*A(u,t)): F:=0: for k from 1 to 10 do F:=map(simplify,
               int(series(subs(A(u,t)=F,DA),u,k),u)); od:
%Y A074060 Cf. A074059. 2nd diagonal is A002662.
%Y A074060 Sequence in context: A141691 A157147 A156920 this_sequence A157637 A157181 
               A029847
%Y A074060 Adjacent sequences: A074057 A074058 A074059 this_sequence A074061 A074062 
               A074063
%K A074060 nonn,tabl
%O A074060 3,5
%A A074060 Margaret A. Readdy (readdy(AT)ms.uky.edu), Aug 16 2002
%E A074060 More terms and Maple code from Eric Rains, Apr 02 2005

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