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A119401 a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n,k). 0

%I

%S 1,0,-3,46,-927,25476,-922715,42240402,-2337537279,147901509928,

%T -9689806983699,464655683171670,44744831894861857,

%U -27559636076854374804,9449663596631181414933,-3046842389019074859527174,1013788651063121586526459905

%N a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n,k).

%F Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1+x)))/(1+x).

%F a(n) = -3*(n-1)*n*a(n-1) - 3*(n-1)^4*a(n-2) - (n-2)^3*(n-1)^3*a(n-3). - _Vaclav Kotesovec_, Jun 08 2019

%t Table[Sum[(-1)^(n - k)*(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] (* _Stefan Steinerberger_, Jun 17 2007 *)

%Y Cf. A119400.

%K easy,sign

%O 0,3

%A _Vladeta Jovovic_, Jul 25 2006

%E More terms from _Stefan Steinerberger_, Jun 17 2007

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Last modified September 28 04:24 EDT 2021. Contains 347698 sequences. (Running on oeis4.)