A065951 Bessel polynomial {y_n}'''(-1).

0, 0, 0, 90, -1890, 36540, -729540, 15507450, -353908170, 8680615020, -228436914420, 6431738433120, -193144902350400, 6166945337372820, -208728050864680620, 7467661073819689470, -281666767117960443870, 11173071188540083124700

Offset: 0

Author

N. J. A. Sloane, Dec 08 2001

Keywords

• sign

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400
• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

Cf. A001518, A001516.

Programs

Mathematica

Join[{0, 0, 0}, Table[48*Binomial[n, 3]*Pochhammer[1/2, n]*(-2)^(n - 3)* Hypergeometric1F1[3 - n, -2*n, -2], {n,3,50}]] (* G. C. Greubel, Aug 15 2017 *)
CoefficientList[Series[(90*t^3/(1 - t)^7)*HypergeometricPFQ[{4, 7/2}, {}, -2*t/(1 - t)^2], {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2017 *)

PARI

for(n=0,50, print1(sum(k=0,n-3, ((n+k+3)!/(8*(n-k-3)!*k!))*(-2)^k ), ", ")) \\ G. C. Greubel, Aug 15 2017

Formula

a(n) = 48*binomial(n,3)*(1/2){n}*(-2)^(n - 3)*hypergeometric1f1(3-n, -2*n, -2), where (a){n} is the Pochhammer symbol. - G. C. Greubel, Aug 15 2017

G.f.: (90*x^3/(1-x)^7)*hypergeometric2f0(4,7/2; - ; -2*x/(1-x)^2). - G. C. Greubel, Aug 16 2017

D-finite with recurrence (-n+3)*a(n) +(-2*n^2+11)*a(n-1) +(-2*n^2+8*n+3)*a(n-2) +(n+1)*a(n-3)=0. - R. J. Mathar, Jul 25 2022