A119394 a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n-1,k-1).

1, 1, -3, 19, -191, 2301, -5579, -2972633, 365848449, -41439009671, 5100344009101, -707810961855909, 111655250271582337, -19997759486622720971, 4047974925567723953349, -920668079777059041167249, 233796999474238422487503361, -65865180249832257997559536143

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Maple

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

Mathematica

Table[Sum[(-1)^(n-k)*(n!/k!)^2*Binomial[n-1, k-1], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *)

Crossrefs

Sequence in context: A141623 A229234 A090354 * A101481 A155805 A218261

Adjacent sequences: A119391 A119392 A119393 * A119395 A119396 A119397

Keyword

easy,sign

Author

Vladeta Jovovic, Jul 25 2006

Extensions

More terms from R. J. Mathar, Jan 21 2008

Status

approved