A065946 Bessel polynomial {y_n}''(-2).

0, 0, 6, -150, 3870, -110670, 3538500, -125941284, 4953759300, -213744815460, 10047637214010, -511403305348650, 28029852267603186, -1646397200571955650, 103190849406195456360, -6875135229835376875560, 485256294032090950981800

Offset

0,3

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..360

Index entries for sequences related to Bessel functions or polynomials

Formula

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

a(n) = 4*n*(n - 1)*(1/2)_{n}*(-4)^(n - 2)*hypergeometric1f1[(2-n, -2*n, -1), where (a)_{n} is the Pochhammer symbol.

E.g.f.: (1/16)*(1 + 4*x)^(-5/2)*((24*x^2 + 20*x + 2)*sqrt(1 + 4*x) + (16*x^3 - 12*x^2 - 24*x - 2))*exp((sqrt(1 + 4*x) -1)/2). (End)

G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; -4*x/(1-x)^2). - G. C. Greubel, Aug 16 2017

Mathematica

Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*(-4)^(n - 2)*
Hypergeometric1F1[2 - n, -2*n, -1], {n, 2, 50}]] (* G. C. Greubel, Aug 14 2017 *)

Prog

(PARI) for(n=0, 50, print1(sum(k=0, n-2, ((n+k+2)!/(4*k!*(n-k-2)!))*(-1)^k), ", ")) \\ G. C. Greubel, Aug 14 2017

Crossrefs

Cf. A001518, A001516.

Sequence in context: A070025 A291110 A246214 * A222051 A285747 A013296

Adjacent sequences: A065943 A065944 A065945 * A065947 A065948 A065949

Keyword

sign

Author

N. J. A. Sloane, Dec 08 2001

Status

approved