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A126930
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Inverse binomial transform of A005043.
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10
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1, -1, 2, -3, 6, -10, 20, -35, 70, -126, 252, -462, 924, -1716, 3432, -6435, 12870, -24310, 48620, -92378, 184756, -352716, 705432, -1352078, 2704156, -5200300, 10400600, -20058300, 40116600, -77558760, 155117520, -300540195, 601080390, -1166803110
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OFFSET
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0,3
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COMMENTS
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Successive binomial transforms are : A005043, A000108, A007317, A064613, A104455 . Hankel transform is A000012.
Moment sequence of the trace of the square of a random matrix in USp(2)=SU(2). If X=tr(A^2) is a random variable (A distributed with Haar measure) then a(n) = E[X^n]. - Andrew V. Sutherland (drew(AT)math.mit.edu), Feb 29 2008
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REFERENCES
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Francesc Fite, Kiran S. Kedlaya, Victor Rotger and Andrew V. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, Arxiv preprint arXiv:1110.6638, 2011
Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
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LINKS
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Table of n, a(n) for n=0..33.
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices.
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FORMULA
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a(n)=(-1)^n*C(n,floor(n/2))=(-1)^n*A001405(n) . a(2*n)=A000984(n), a(2*n+1)=-A001700(n).
a(n) = (1/Pi)*Integral_{t=0..Pi}(2cos(2t))^n*2sin^2(t) dt - Andrew V. Sutherland (drew(AT)math.mit.edu), Feb 29 2008, Mar 09 2008
a(n)= (-2)^n + Sum_{k=0..n-1}a(k)*a(n-1-k), a(0)=1. [Philippe DELEHAM, Dec 12 2009]
G.f.: (1+2*x-sqrt(1-4*x^2))/(2*x*(1+2*x)). - Philippe Deléham, Mar 01 2013
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CROSSREFS
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Cf. A126120, A126869.
Sequence in context: A037031 A056202 A001405 * A210736 A036557 A173125
Adjacent sequences: A126927 A126928 A126929 * A126931 A126932 A126933
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KEYWORD
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sign
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AUTHOR
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Philippe DELEHAM, Mar 17 2007
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STATUS
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approved
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