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Search: id:A119400
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| A119400 |
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a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n,k). |
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+0
1
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| 1, 2, 13, 172, 3809, 126526, 5874517, 362848088, 28744087297, 2839192902874, 341922922464701, 49297062811573732, 8380916229314577313, 1658770724530766046422, 378056469777362366873989
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OFFSET
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0,2
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FORMULA
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Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1-x)))/(1-x).
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MATHEMATICA
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Table[Sum[(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 17 2007
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CROSSREFS
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Adjacent sequences: A119397 A119398 A119399 this_sequence A119401 A119402 A119403
Sequence in context: A143851 A088316 A006905 this_sequence A137610 A073178 A062156
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 25 2006
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 17 2007
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