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A119394
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a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n-1,k-1).
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1
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1, 1, -3, 19, -191, 2301, -5579, -2972633, 365848449, -41439009671, 5100344009101, -707810961855909, 111655250271582337, -19997759486622720971, 4047974925567723953349, -920668079777059041167249, 233796999474238422487503361, -65865180249832257997559536143
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum_{>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1+x))).
Recurrence: a(n) = -(3*n^2 - 5*n + 1)*a(n-1) - (n-2)*(n-1)^2*(3*n-4)*a(n-2) - (n-3)*(n-2)^3*(n-1)^2*a(n-3). - Vaclav Kotesovec, Mar 02 2014
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MAPLE
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A119394 := proc(n) local k ; add((-1)^(n-k)*(n!/k!)^2*binomial(n-1, k-1), k=0..n) ; end: seq(A119394(n), n=0..20) ; # R. J. Mathar, Jan 21 2008
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MATHEMATICA
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Table[Sum[(-1)^(n-k)*(n!/k!)^2*Binomial[n-1, k-1], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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