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A115330
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E.g.f: exp(x/(1-4*x))/sqrt(1-16*x^2).
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1
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1, 1, 25, 169, 5329, 78961, 3031081, 71995225, 3275616289, 108078535009, 5707994717881, 241468632426121, 14559189135946225, 750901957984356049, 50993055118129961929, 3098872535897951163961, 234376094007794247481921
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OFFSET
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0,3
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COMMENTS
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Term-by-term square of sequence with e.g.f.: exp(x+m/2*x^2) is given by e.g.f.: exp(x/(1-m*x))/sqrt(1-m^2*x^2) for all m.
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LINKS
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FORMULA
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Equals term-by-term square of A115329 which has e.g.f.: exp(x+2*x^2).
D-finite with recurrence: a(n) = (4*n-3)*a(n-1) + 4*(n-1)*(4*n-3)*a(n-2) - 64*(n-1)*(n-2)^2*a(n-3). - Vaclav Kotesovec, Jun 26 2013
a(n) ~ 2^(2*n-1)*n^n*exp(sqrt(n)-n-1/8) * (1 + 25/(96*sqrt(n))). - Vaclav Kotesovec, Jun 26 2013
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MATHEMATICA
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CoefficientList[Series[E^(x/(1-4*x))/Sqrt[1-16*x^2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)
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PROG
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(PARI) a(n)=local(m=4); n!*polcoeff(exp(x/(1-m*x+x*O(x^n)))/sqrt(1-m^2*x^2+x*O(x^n)), n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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