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A092690
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Row sums of triangle A092689, which is related to the central trinomial coefficients (A002426).
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2
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1, 2, 7, 22, 71, 226, 717, 2262, 7107, 22246, 69413, 215986, 670441, 2076686, 6420403, 19816362, 61070499, 187953174, 577742469, 1773918642, 5441141589, 16674016758, 51052484343, 156188410098, 477487110429, 1458741494826
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: a(n) = n!* [x^n] exp(x)*((1+x)*BesselI(0, 2*x)+x*BesselI(1, 2*x)). - Peter Luschny, Aug 25 2012
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MATHEMATICA
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With[{nn = 50}, CoefficientList[Series[Exp[x]*((1 + x)*BesselI[0, 2*x] + x*BesselI[1, 2*x]), {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Feb 27 2017 *)
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PROG
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(PARI) {T(n, k)=if(n<0 || k>n, 0, if(n==0 && k==0, 1, if(n==1 && k<=1, 1, if(k==n-1, T(n-1, 0), if(k==n, T(n, 0), 2*T(n-1, k)+T(n-1, k+1))))))} a(n)=sum(k=0, n, T(n, k))
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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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