A065923 - OEIS

%I #24 Aug 17 2017 06:13:21

%S 1,-2,19,-287,6046,-163529,5402503,-210861146,9494154073,

%T -484412718869,27621019129606,-1740608617884047,120129615653128849,

%U -9011461782602547722,730048534006459494331,-63523233920344578554519,5908390803126052265064598

%N Bessel polynomial y_n(-3).

%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.

%H G. C. Greubel, <a href="/A065923/b065923.txt">Table of n, a(n) for n = 0..345</a>

%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>

%F a(n) = -(6*n-3)*a(n-1) + a(n-2) for n >= 2. - _Sergei N. Gladkovskii_, May 17 2013

%F G.f.: 1/Q(0), where Q(k)= 1 - x + 3*x*(k+1)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, May 17 2013

%F From _G. C. Greubel_, Aug 14 2017: (Start)

%F a(n) = (1/2)_{n} * (-3)^n *hypergeometric1f1(-n; -2n; -2/3), where (a)_{n} is the Pochhammer symbol.

%F E.g.f.: (1+6*x)^(-1/2) * exp((sqrt(1+6*x) - 1)/3). (End)

%F G.f.: (1/(1-x))*hypergeometric2f0(1,1/2; - ; -6*x/(1-x)^2). - _G. C. Greubel_, Aug 16 2017

%p f:= gfun:-rectoproc({a(n)= -(6*n-3)*a(n-1) + a(n-2),a(0)=1,a(1)=-2},a(n),remember):

%p map(f, [$0..50]); # _Robert Israel_, Aug 16 2017

%t Table[Pochhammer[1/2, n]*(-6)^n*Hypergeometric1F1[0 - n, -2*n, -2/3], {n, 0, 50}] (* _G. C. Greubel_, Aug 14 2017 *)

%o (PARI) for(n=0,50, print1(sum(k=0,n, ((n+k)!/(k! * (n-k)!))*(-3/2)^k), ", ")) \\ _G. C. Greubel_, Aug 14 2017

%Y Polynomial coefficients are in A001498.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Dec 08 2001