A065923 Bessel polynomial y_n(-3).

1, -2, 19, -287, 6046, -163529, 5402503, -210861146, 9494154073, -484412718869, 27621019129606, -1740608617884047, 120129615653128849, -9011461782602547722, 730048534006459494331, -63523233920344578554519, 5908390803126052265064598

Offset

0,2

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..345

Index entries for sequences related to Bessel functions or polynomials

Formula

a(n) = -(6*n-3)*a(n-1) + a(n-2) for n >= 2. - Sergei N. Gladkovskii, May 17 2013

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

From G. C. Greubel, Aug 14 2017: (Start)

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

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

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

Maple

f:= gfun:-rectoproc({a(n)= -(6*n-3)*a(n-1) + a(n-2), a(0)=1, a(1)=-2}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Aug 16 2017

Mathematica

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

Prog

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

Crossrefs

Polynomial coefficients are in A001498.

Sequence in context: A191806 A349721 A252710 * A293946 A365652 A094476

Adjacent sequences: A065920 A065921 A065922 * A065924 A065925 A065926

Keyword

sign

Author

N. J. A. Sloane, Dec 08 2001

Status

approved