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A119399
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a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n-1,k-1).
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0
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1, 1, 5, 55, 1057, 31301, 1319581, 74996755, 5521809665, 510921831817, 58003632177301, 7924389193344911, 1282139184447959905, 242395881776602480525, 52937407769332221775277
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Sum_{>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1-x))).
Special values of hypergeometric function of type 1F2. In Maple notation : a(n)=((n!)^2)*hypergeom([1-n],[2,2],-1), n=0,1... . This sequence arises in exponentiating the operator D=d(x^2)(d^2), where d=d/dx - Karol A.Penson (penson(AT)lptl.jussieu.fr) Nov 22 2008 [From Karol A. Penson (penson(AT)lptl.jussieu.fr), Nov 22 2008]
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CROSSREFS
| Sequence in context: A006150 A140049 A130031 * A177557 A158690 A192723
Adjacent sequences: A119396 A119397 A119398 * A119400 A119401 A119402
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 25 2006
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