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A119401
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a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n,k).
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0
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1, 0, -3, 46, -927, 25476, -922715, 42240402, -2337537279, 147901509928, -9689806983699, 464655683171670, 44744831894861857, -27559636076854374804, 9449663596631181414933, -3046842389019074859527174, 1013788651063121586526459905
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1+x)))/(1+x).
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MATHEMATICA
| Table[Sum[(-1)^(n - k)*(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
| Sequence in context: A037105 A196137 A059624 * A124135 A193420 A000576
Adjacent sequences: A119398 A119399 A119400 * A119402 A119403 A119404
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KEYWORD
| easy,sign
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 25 2006
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 17 2007
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